Question

Prove that (coseec theta-sin theta)(tan theta+cot theta)=1

Answer 1

$\huge\bigstar\underline\mathbf{STEP\: BY \:STEP \:EXPLANATION }$

To prove,

(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ)=1

Proof:

LHS =(1/sin θ - sin θ)(1/cos θ - cos θ)(tan θ+1/tan θ)

=(1-sin²θ)/sinθ (1-cos²θ)/cosθ(1+tan²θ)/tanθ

=(cos²θ)/sinθ (sin²θ)/cosθ sec²θ/tanθ

=cos θ sin θ (1/cos²θ)/(sinθ/cosθ)

=cos θ sin θ(1/cos²θ)(cosθ/sinθ)

=cos θ sin θ (cos θ/sin θ cos²θ)

=cos θ sin θ (1/sin θ cos θ)

=cos θ sin θ/sin θ cos θ

=1=RHS

∴ Hence proved.

Answer 2

Answer:

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