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What is (sintheta+1)/(costheta) equal t...

What is `(sintheta+1)/(costheta)` equal to ?

A

`(sintheta+costheta-1)/(sintheta+costheta+1)`

B

`(sintheta+costheta+1)/(sintheta+costheta-1)`

C

`(sintheta-costheta-1)/(sintheta+costheta+1)`

D

`(sintheta-costheta+1)/(sintheta+costheta-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Consider `(1+sintheta)/(costheta)=(1+sintheta)/(costheta)=(1+(2"tan"(theta)/(2))/(1+"tan"^(2)(theta)/(2)))/((1-"tan"^(2)(theta)/(2))/(1+"tan"^(2)(theta)/(2)))`
`(becausesin2theta=(2tantheta)/(1+tan^(2)theta)andcos2 theta=(1-tan^(2)theta)/(1+tan^(2)theta))`
`=((1+"tan"(theta)/(2))^(2))/((1+"tan"(theta)/(2))(1+"tan"(theta)/(2)))`
`=(1+"tan"(theta)/(2)"cos"(theta)/(2)+2"sin"^(2)(theta)/(2))/(2"sin"(theta)/(2) "cos "(theta)/(2)-2" sin"^(2)(theta)/(2))`
`=(sintheta+1-costheta)/(sintheta-1+costheta)`
`(becausesin2 theta=2sinthetacosthetaand cos2 theta=1-2sin^(2)theta)`
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