If tan θ=125find the value of 1+sin θ1−sin θ

If tan θ=125find the value of 1+sin θ1−sin θ
|

If tan θ=125,find the value of 1+sin θ1sin θ

Please scroll down to see the correct answer and solution guide.

Right Answer is:

SOLUTION

g i v e n
space space space space space tan theta equals 12 over 5
1 plus tan squared theta equals s e c squared theta
1 plus open parentheses 12 over 5 close parentheses squared equals s e c squared theta
1 plus 144 over 25 equals s e c squared theta
169 over 25 equals s e c squared theta
s e c theta equals 13 over 5
s o space cos theta equals 5 over 13
a l s o space
space space space space space space space sin squared theta plus cos squared theta equals 1
space space space space space space space space sin squared theta plus open parentheses 5 over 13 close parentheses squared equals 1
space space space space space space space space space sin squared theta equals 1 minus 25 over 169
space space space space space space space space space space sin squared theta equals 144 over 169
space space space space space space space space space space sin theta equals 12 over 13
s o
space space space space space space space space space space fraction numerator 1 plus sin theta over denominator 1 minus sin theta end fraction equals fraction numerator 1 plus begin display style 12 over 13 end style over denominator 1 minus begin display style 12 over 13 end style end fraction
space space space space space space space space space space space fraction numerator 1 plus sin theta over denominator 1 minus sin theta end fraction equals fraction numerator 13 plus 12 over denominator 13 minus 12 end fraction
space space space space space space space space space space space space fraction numerator 1 plus sin theta over denominator 1 minus sin theta end fraction equals 25