Question

If 7 \cosec( \alpha ) - 3 \cot( \alpha ) = 77cosec(α)−3cot(α)=7
then prove that
7 \cot( \alpha ) - 3 \cosec( \alpha ) = 37cot(α)−3cosec(α)=3

Please solve the qûēßtìøñ

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Answer 1

Given---> 7 Cosecθ - 3 Cotθ = 7

To prove---> 7 Cotθ - 3 Cosecθ = 3

Proof ---> ATQ,

7 Cosecθ - 3 Cotθ = 7

=> 7 Cosecθ - 7 = 3 Cotθ

=> 7 ( Cosecθ - 1 ) = 3 Cotθ

Multiplying both sides by ( Cosecθ - 1 )

=> 7(Cosecθ - 1) (Cosecθ + 1) = 3 Cotθ(Cosecθ+ 1 )

We have an identiy , a² - b² = ( a + b ) ( a - b ) , applying it in LHS, we get,

=> 7 { ( Cosec²θ - ( 1 )² } = 3 Cotθ ( Cosecθ + 1 )

=> 7 ( Cosec²θ - 1 ) = 3 Cotθ ( Cosecθ + 1 )

We know that , Cosec²A - 1 = Cot²A , applying it in LHS , we get,

=> 7 Cot²θ = 3 Cotθ ( Cosecθ + 1 )

Cotθ is cancel out from both sides and we get,

=> 7 Cotθ = 3 ( Cosecθ + 1 )

=> 7 Cotθ = 3 Cosecθ + 3

=> 7 Cotθ - 3 Cosecθ = 3

Hence Proved

Answer 2

Answer:

Answer in attachment.

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