Question No. 15, Question No. 12, Question No. 16

Lesson#5
Toolkit for Exercise 9.4
Prove the following identity:
Question No. 15
Q15: (2 tanθ)/(1+tan^2 θ)=2 sinθ cosθ
Question No. 12
Q12: (cot^2 θ−1" " )/(1+cot^2 θ)=2 cos^2 θ−1
Question No. 16
Q16: (1−sinθ)/cosθ=cosθ/(1+sinθ)
Solution:
Consider L.H.S
L.H.S=(1−sinθ)/cosθ
Multiply and divide by 1+sin⁡θ
=((1−sinθ).)/cosθ ((1+sinθ))/((1+sinθ) )
=(1−sin^2 θ)/cosθ(1+sinθ)
=(cos^2 θ)/cosθ(1+sinθ)
=cosθ/(1+sinθ)=R.H.S
Exercise No. 9.4
Chapter No.9
Fundamentals of Trignometry
maths
part 1