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Question
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
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Solution
LHS = `(sec θ - 1)/(sec θ + 1)`
= `(1/cos θ - 1)/(1/cos θ + 1)`
= `(1 - cos θ)/(1 + cos θ)`
= `(1 - cos θ xx ( 1 + cos θ))/(1 + cos θ xx (1 + cos θ))`
= `(1 - cos^2 θ)/(1 + cos θ)^2`
= `(sin^2 θ)/(1 + cos θ)^2`
= `((sin θ)/(1 + cos θ ))^2`
= RHS
RELATED QUESTIONS
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
