Question

Prove the following trigonometric identities:
(cosecA-sinA)(secA-cosA)(tanA+cotA)=1

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

To prove --->

(CosecA - SinA) (SecA - CosA) (tanA + CotA ) = 1

Proof----> We know that,

CosecA = 1 / SinA

SecA = 1 / CosA

First we solve first bracket of LHS

( CosecA - SinA ) = ( 1 / SinA - SinA )

= ( 1 - Sin²A ) / SinA

We know that, 1 - Sin²A = Cos²A , applying it , we get

= Cos²A / SinA

Now we solve second bracket,

( SecA - CosA ) = ( 1 / CosA - CosA )

= ( 1 - Cos²A ) / CosA

We know that, 1 - Cos²A = Sin²A , applying it we get,

= Sin²A / CosA

Now we solve third bracket,

( tanA + CotA ) = ( SinA / CosA + CosA / SinA )

= ( Sin²A + Cos²A ) / SinA CosA

We know that , Sin²θ + Cos²θ = 1 , we get,

= 1 / SinA CosA

Now taking LHS ,

(CosecA - SinA) ( SecA - CosA) ( tanA + CotA)

Putting values of all brackets , we get ,

= (Cos²A / SinA) ( Sin²A / CosA) ( 1 / SinA CosA )

= Cos²A Sin²A / Cos²A Sin²A

= 1 = RHS