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Question
Select the correct option from the given alternatives:
`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)` equals
Options
0
1
sin θ
cos θ
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Solution
cos θ
Explanation:
`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)`
= `1 - (1 - cos^2theta)/(1 + costheta) + (1 - cos^2theta)/(sintheta(1 - costheta)) - sintheta/(1 - costheta)`
= `1 - (1 - costheta) + sintheta/(1 - costheta) - sintheta/(1 - costheta)`
= cos θ
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