Question

Prove that: (cosecθ - sin θ) ( sec θ - cosθ) (tan θ+ cot θ) =1
(Class 10 Maths Sample Question Paper)

Answer 1

SOLUTION;
LHS=

(cosecθ - sin θ) ( sec θ - cosθ)(tan θ+ cot θ)

= (1/sinθ - sinθ) (1/cosθ - cosθ)(sinθ/cosθ+cosθ/sinθ)
= (( 1- sin²θ)/sinθ) ((1- cos²θ)/cosθ) ((sin²θ+cos²θ)/sinθ.cosθ)
=( Cos²θ/sinθ)(sin²θ/Cosθ) (1/sinθ.cosθ)

[ 1- sin²θ = cos²θ, 1- cos²θ= sin²θ, sin²θ+cos²θ= 1]

= (cosθ . sinθ) / ( sinθ.cosθ)
= 1

= RHS

HOPE THIS WILL HELP YOU....

Answer 2

Hi friend,

We need to prove that

(cosecθ - sin θ) ( sec θ - cosθ) (tan θ+ cot θ) =1

(cosecθ - sin θ) ( sec θ - cosθ)(tan θ+ cot θ)

= (1/sinθ - sinθ) (1/cosθ - cosθ)(sinθ/cosθ+cosθ/sinθ)

= (( 1- sin²θ)/sinθ).
((1- cos²θ)/cosθ).
((sin²θ+cos²θ)/sinθ.cosθ)

=( Cos²θ/sinθ)(sin²θ/Cosθ) (1/sinθ.cosθ)

[ 1- sin²θ = cos²θ, 1- cos²θ= sin²θ, sin²θ+cos²θ= 1]

= (cosθ . sinθ) / ( sinθ.cosθ)

= 1.

Hope this helped you a little!!!