Advertisements
Advertisements
Question
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Advertisements
Solution
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2`
= `(sinθ/cosθ + 1/cosθ)^2 + (sinθ/cosθ - 1/cosθ)^2`
= `((sinθ + 1)/cosθ)^2 + ((sinθ - 1)/cosθ)^2`
= `(sinθ + 1)^2/(cos^2θ) + (sinθ - 1)^2/cos^2θ`
= `((sinθ + 1)^2 + (sinθ - 1)^2)/cos^2A`
= `(sin^2θ + 1 + 2sinθ + sin^2θ + 1 - 2sinθ)/(1 - sin^2θ)`
= `(2(1 + sin^2θ))/(1 - sin^2θ)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2 + n2) = (a2 + b2).
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
9 sec2 A − 9 tan2 A is equal to
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
(sec θ + tan θ) . (sec θ – tan θ) = ?
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
