# TRIGONOMETRY PROVING PROBLEM FOR CLASS 11

## About "Trigonometry Proving Problems For Class 11"

Trigonometry Proving Problems For Class 11

Here we are going to see some practice questions trigonometry.

## Trigonometry Proving Problems For Class 11 - Questions

Question 1 :

If A + B = 45, show that (1 + tan A) (1 + tan B) = 2.

Solution :

A + B = 45

tan (A + B)  =  tan 45

(tan A + tan B)/(1 - tan A tan B)  =  1

tan A + tan B  =  1 - tan A tan B

Add tan A tan B on both sides

tan A + tan B + tan A tan B =  1

tan A + tan B(1 + tan A)  =  1

1 + tan A + tan B(1 + tan A)  =  1 + 1

(1 + tan A) (1 + tan B)  =  2

Hence proved.

Question 2 :

Prove that (1 + tan 1)(1 + tan 2)(1 + tan 3) ................(1 + tan 44) is a multiple of 4.

Solution :

=  (1 + tan 1)(1 + tan 2)(1 + tan 3) ................(1 + tan 44)

=  (1 + tan 1)(1 + tan 44)(1 + tan 2)(1 + tan 43)(1 + tan 3)(1 + tan 42)................

If A + B  =  45then (1 + tan A)(1 + tan B)  =  2

In the first two terms, we have 1 instead of A and 44 instead of B.

In a same manner, in third and 4th terms we have 2 instead of A and 43 instead of B. So, we get

=  2 (2) (2)........................

It is a multiple of 4.

Question 3 :

Prove that tan (π/+ θ) - tan (π/− θ)  =  2 tan 2θ.

Solution :

tan (π/+ θ)  =  (tan π/4 + tan θ) / (1 - tan π/4 tan θ)

tan (π/4 + θ)  =  (1 + tan θ) / (1 - tan θ)--------(1)

tan (π/4 - θ)  =  (tan π/4 - tan θ) / (1 + tan π/4 tan θ)

tan (π/4 - θ)  =  (1 - tan θ) / (1 + tan θ)--------(2)

(1) - (2)

tan (π/4 + θ) - tan (π/4 - θ)

=  [(1 + tan θ) / (1 - tan θ)] - [(1 - tan θ) / (1 + tan θ)]

=  [(1 + tan θ)2 -(1 - tan θ)2]/(1 - tan θ)(1 + tan θ)

=  [(1+tan2θ+2tanθ) -(1+tan2θ-2tanθ)]/(1-tan θ)(1+tan θ)

=  4tanθ/(1-tan2 θ)

=  2[2tanθ/(1-tan2 θ)]

=  2 tan 2θ

Hence proved.

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