Question

Prove that (cosec ⁡θ - sin⁡θ) (sec⁡θ - cos⁡θ) ( tan⁡θ + cot⁡θ )=1​

Answer 1

Answer:

Step-by-step explanation:

easy

I won't give you the proper solution but

convert tan, cot, sec and cosec in terms of sin and cos

cosec = 1/ sin

sec = 1/cos

tan= sin/cos

cot= cos/sin

And remember to use the identity

1-sin^2 = cos^2

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

                 Hope it Helps!!

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