
cos(A+B).cos(A-B) is identically equal to:
(a)
(b)
(c)
(d) cos2A.sin2B
Answer
535.2k+ views
Hint: Start by applying the formula of cos(A+B) and cos(A-B) followed by factorisation at the end to reach the required expression.
Complete step-by-step answer:
Before starting with the solution to the above question, let us first discuss the important trigonometric formulas that we are going to be using in our solution.
.
.
We are now moving to the expression given in the question.
cos(A+B).cos(A-B).
When we apply the formula of cos(X+Y) and cos(X-Y) to the expression, we get
Now moving on to multiplying and opening the brackets, the above expression becomes,
Now on applying the formula and , our expression becomes:
Again multiplying and opening the brackets, the expression comes out to be:
But no option is matching with our final expression.
So, again using the formula and to convert the expression to a suitable form. On doing so our equation becomes:
So, we can say that cos(A+B).cos(A-B) is identically equal to .
Hence, option (b) is the correct answer.
Note: It is preferred to keep the expression as neat as possible by eliminating all the removable terms as the larger is the number of terms in your expression more is the probability of making a mistake. In trigonometry, it is often seen that many formulas lead to the same answer. However, the complexity of the question varies with the selection of the formula. The wiser the selection of formula, the easier the question will be to solve.
Complete step-by-step answer:
Before starting with the solution to the above question, let us first discuss the important trigonometric formulas that we are going to be using in our solution.
We are now moving to the expression given in the question.
cos(A+B).cos(A-B).
When we apply the formula of cos(X+Y) and cos(X-Y) to the expression, we get
Now moving on to multiplying and opening the brackets, the above expression becomes,
Now on applying the formula
Again multiplying and opening the brackets, the expression comes out to be:
But no option is matching with our final expression.
So, again using the formula
So, we can say that cos(A+B).cos(A-B) is identically equal to
Hence, option (b) is the correct answer.
Note: It is preferred to keep the expression as neat as possible by eliminating all the removable terms as the larger is the number of terms in your expression more is the probability of making a mistake. In trigonometry, it is often seen that many formulas lead to the same answer. However, the complexity of the question varies with the selection of the formula. The wiser the selection of formula, the easier the question will be to solve.
Latest Vedantu courses for you
Grade 7 | CBSE | SCHOOL | English
Vedantu 7 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Explain why it is said like that Mock drill is use class 11 social science CBSE

The non protein part of an enzyme is a A Prosthetic class 11 biology CBSE

Which of the following blood vessels in the circulatory class 11 biology CBSE

What is a zygomorphic flower Give example class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

The deoxygenated blood from the hind limbs of the frog class 11 biology CBSE
