JEE Main Registration 2025 Session 1 (Open) - Link, Last Date, Fees, How to Apply

Sum-to-Product and Product-to-Sum Formulas - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Eligibility Criteria

Application Process

Preparation Tips

Counselling Process

Quick Facts

11 Questions around this concept.

Solve by difficulty

The product of $4\cos\left ( \frac{5x}{2} \right )\cos\left ( \frac{3x}{2} \right )$ as a sum is

A

$2\cos\ x+2\cos\ 4x$

B

$2\cos\ x-2\cos\ 4x$

C

$2\cos\ x+4\cos\ 4x$

D

$2\cos\ x-4\cos\ 4x$

The value of $\cos 5 x-\cos 3 x$ is

A

$4 \sin ^2 x$

B

$2 \sin ^2 x$

C

$-4 \sin ^2 x$

D

$-2 \sin ^2 x$

Concepts Covered - 1

Sum-to-Product and Product-to-Sum Formulas

Product into Sum/Difference

$\\\begin{array}{l}{1.\;\;2\cos \alpha \cos \beta=[\cos (\alpha-\beta)+\cos (\alpha+\beta)]} \\ {2.\;\;2\sin \alpha \sin \beta=[\cos (\alpha-\beta)-\cos (\alpha+\beta)]}\end{array}\\\begin{array}{l}{3.\;\;2\sin \alpha \cos \beta=[\sin (\alpha+\beta)+\sin (\alpha-\beta)]} \\ {4.\;\;2\cos \alpha \sin \beta=[\sin (\alpha+\beta)-\sin (\alpha-\beta)]}\end{array}$

Proof:

We can derive the product-to-sum formula from the sum and difference identities

$\begin{aligned} \cos \alpha \cos \beta+\sin \alpha \sin \beta =\cos (\alpha-\beta) \\+\cos \alpha \cos \beta-\sin \alpha \sin \beta =\cos (\alpha+\beta) \\\overline{2 \cos \alpha \cos \beta =\cos (\alpha-\beta)+\cos (\alpha+\beta)\;\;\;} \end{aligned}$

$\\\mathrm{\;\;\;\;\;\sin \left(\alpha +\beta \right)=\sin \left(\alpha \right)\cos \left(\beta \right)+\cos \left(\alpha \right)\sin \left(\beta \right)}\\\mathrm{+\;\;\sin \left(\alpha -\beta \right)=\sin \left(\alpha \right)\cos \left(\beta \right)-\cos \left(\alpha \right)\sin \left(\beta \right)}\\\mathrm{\overline{\;\;\;\;\;\;\;\;\;\sin \:\left(\alpha \:+\beta \:\right)+\sin \left(\alpha -\beta \right)=2\sin \left(\alpha \right)\cos \left(\beta \right)\;\;\;\;\;\;}}$

$\\\mathrm{\;\;\;\;\;\cos (\alpha-\beta)=\cos \alpha \cos \beta+\sin \alpha \sin \beta}\\\mathrm{-\;\;\cos (\alpha+\beta)=-(\cos \alpha \cos \beta-\sin \alpha \sin \beta)}\\\mathrm{\overline{\;\;\;\;\;\;\;\;\;\cos (\alpha-\beta)-\cos (\alpha+\beta)=2 \sin \alpha \sin \beta\;\;\;\;\;\;}}$

Study it with Videos

Sum-to-Product and Product-to-Sum Formulas

Study other Related Concepts

Sum-to-Product and Product-to-Sum Formulas Current Topic

Measuring Angles

Trigonometric Ratios

Trigonometric Identities

Sign of Trigonometric Functions

Graphs of General Trigonometric Functions

Trigonometric Ratios of Allied Angles

Trigonometric Ratios of Compound Angles

Sum-to-Product and Product-to-Sum Formulas

Product To Sum Formulas

Double Angle Formulas

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Sum-to-Product and Product-to-Sum Formulas

Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

Page No. : 3.8

Line : 36

Clear your Basics with NCERT

NCERT Solutions for Class 11 Maths (2024-25)

July 04, 2019

NCERT Solutions for Class 12 Maths - Get Free PDFs 2024-25

June 10, 2019

E-books & Sample Papers

JEE Main 2025 Math Syllabus

8261+ Downloads

JEE Main 2025 Physics Syllabus

20371+ Downloads

Get Answer to all your questions

JEE Main Articles

List of B.Tech Colleges Accepting 91-95 Percentile in JEE Main 2024

Nov 08, 2024

JEE Main 2025 Photo Size and Signature Guidelines - Passport Size Photo Required for IIT JEE

Nov 08, 2024

BTech Admission 2024: Entrance Exams, Eligibility Criteria, Fees, Admission Process, Top Colleges

Nov 08, 2024

NITs Cutoff 2025 for B.Tech CSE (Computer Science and Engineering)

Nov 08, 2024

JEE Main Information Bulletin 2025 Out - Direct Link To Download PDF

Nov 08, 2024

Is 75% Criteria Removed from JEE Main 2025? - Check Latest Updates

Nov 08, 2024

JEE Main 2025 New Rules Announced by NTA - Check Latest Changes, Guidelines

Nov 08, 2024

Top 10 Engineering Entrance Exams in India 2025 - BTech Exams after 12th

Nov 08, 2024

B.Tech/B.Arch Admissions OPEN

UPES B.Tech Admissions 2025

Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements

Integral University B.Tech Admissions 2024

NAAC A+ Accredited | Highest CTC 12 LPA | Scholarships Available

Parul University B.Tech Admissions 2025

Parul University B.Tech Admissions 2025

India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package

Dayananda Sagar University B.Tech Admissions 2025

Dayananda Sagar University B.Tech Admissions 2025

60+ Years of Education Legacy | UGC & AICTE Approved | Prestigious Scholarship Worth 6 Crores | H-CTC 35 LPA

Lovely Professional University B.Tech Admissions 2025

Lovely Professional University B.Tech Admissions 2025

India's Largest University | NAAC A++ Accredited | 100% Placement Record | Highest Package Offered : 3 Cr PA

Atlas SkillTech University | B.Tech Admissions

Atlas SkillTech University | B.Tech Admissions

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

View All Application Forms

News and Notifications

3 days ago :

NTA has announced the JEE Main exam date 2025 for sessions 1 and 2.

October 18, 2024 - 09:55 AM IST :

NTA has changed the JEE Main 2025 exam pattern.

BTech Admissions 2025 LIVE: JEE Main, MET registrations open; AEEE, VITEEE dates out

November 08, 2024 - 04:52 PM IST

BTech Admissions 2025: JEE Main registration last date, direct link

November 07, 2024 - 10:09 PM IST

JEE Main 2025 Registration: NTA issues advisory for Aadhaar authentication, name mismatch issues

November 06, 2024 - 05:53 PM IST

BTech Admissions 2025: JEE Main, AEEE registration underway; latest updates

November 05, 2024 - 10:30 PM IST

JEE aspirant found dead in Kota PG; police deny suicide

November 04, 2024 - 09:34 PM IST

JEE Main Syllabus 2025: Topic-wise weightage, marks for physics, chemistry, mathematics

November 04, 2024 - 06:11 PM IST

BTech Admissions 2025 LIVE: AEEE, JEE Mains registration underway; latest updates on MET, SRMJEE, VITEEE

November 04, 2024 - 10:49 AM IST

Download Careers360 App

All this at the convenience of your phone

Regular Exam Updates
Best College Recommendations
College & Rank predictors
Detailed Books and Sample Papers
Question and Answers

Scan and download the app

OR

Joint Entrance Examination (Main)

JEE Main 2025 Sample Papers