Prove that : (Sin(90° - θ) Tan(90° - θ) Sec (90° - θ))/(Cosec θ. Cos θ. Cot θ) = 1

Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`

Sum

LHS = `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`

= `(cosec θ. cos θ. cot θ)/(cosec θ. cos θ. cot θ)`
= 1
= RHS
Hence proved.

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Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2

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`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`

Prove the following identities:

cosec A(1 + cos A) (cosec A – cot A) = 1

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`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`

Prove the following identities:

`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`

Prove that

`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`

Prove the following identity :

`((1 + tan^2A)cotA)/(cosec^2A) = tanA`

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`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`

Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos²θ.

The value of tan A + sin A = M and tan A - sin A = N.

The value of `("M"^2 - "N"^2) /("MN")^0.5`