Question

if tan theta =a/b
Find cos theta +sin theta/cos theta-sin theta

Answer 1

Answer:

tan theta=a/b

therefore,  cos theta +sin theta/cos theta-sin theta

=(cos theta/cos theta +sin theta/cos theta -cos theta)/(cos theta/cos theta-sin      theta/cos theta)

=1+tan theta/1-tan theta                 [as, sin theta/cos theta=tan theta]

=(1+a/b)/(1-a/b)

=$\frac{b+a}{b}$×$\frac{b}{b-a}$

=$\frac{b+a}{b-a}$                               (Answer.)

Answer 2

Step-by-step explanation:

theta = ø

tan ø = a/b

so, sin ø = a/√(a²+b²)

and, cos ø = b√(a²+b²)

(cos ø + sin ø) = (a+b)/√(a²+b²)

(cos ø - sin ø) = (a-b)/√(a²+b²)

so, (cos ø+sin ø)/(cos ø-sin ø)

= [(a+b)/√(a²+b²)]×[√(a²+b²)/(a-b)]

= (a+b)/(a-b)

I hope this is a helpful answer....