Question

9. if tan x = a / b, the (cOS X + sin x) /
(COS X - sin x) = ?​

Answer 1

Answer:

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Answer 2

Answer :-

( cos x + sin x) / ( cos x - sin x) = ( b + a ) / ( b - a )

Solution :-

tan x = a/b = P / B

Here,

• P = a
• B = b

Finding hypotenuse ( H )

By pythagoras theorem

==> H² = P² + B²

==> H² = a² + b²

==> H = √( a² + b² )

Finding cos x and sin x

sin x = P / H

= a / √( a² + b² )

cos x = B / H

= b / √( a² + b² )

Finding ( cos x + sin x) / (cos x - sin x)

$\rm \dfrac{cosx + sinx}{cosx - sinx} = \dfrac{ \dfrac{b}{ \sqrt{ {a}^{2} + {b}^{2} }} + \dfrac{a}{ \sqrt{ {a}^{2} + {b}^{2} } } }{ \dfrac{b}{ \sqrt{ {a}^{2} + {b}^{2} } } - \dfrac{a}{ \sqrt{ {a}^{2} + {b}^{2} } } }$

$\rm = \dfrac{ \dfrac{b+ a}{ \sqrt{ {a}^{2} + {b}^{2} }} }{ \dfrac{b - a}{ \sqrt{ {a}^{2} + {b}^{2} } } }$

$\rm = \dfrac{ b + a }{b - a }$

Therefore the required answer is found.