Advertisements
Advertisements
Question
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Solution
`(sec theta - 1)/(sec theta + 1)`
`= (1/cos theta - 1)/(1/cos theta + 1)`
= `((1 - cos theta)/cos theta)/((1 + cos theta)/cos theta)`
`= (1 - cos theta)/(1 +cos theta)`
`= (1 - cos theta)/(1 + cos theta) xx (1 + cos theta)/(1+ cos theta)`
`= (1 - cos^2 theta)/(1 + cos theta)^2`
`= sin^2 theta/(1 + cos theta)^2`
`= [sin theta/(1 + cos theta)]^2`
=RHS
Hence proved.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
What is the value of 9cot2 θ − 9cosec2 θ?
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
