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Question
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
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Solution
L.H.S. = `cos θ/(1 - sin θ)`
= `(cos θ(1 + sin θ))/((1 - sin θ)(1 + sin θ))`
= `(cos θ(1 + sin θ))/(1 - sin^2θ)`
= `(cos θ(1 + sin θ))/(cos^2 θ)`
= `( 1 + sin θ)/cos θ`
Hence proved.
RELATED QUESTIONS
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
If tanθ `= 3/4` then find the value of secθ.
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
