Advertisements
Advertisements
Question
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
Advertisements
Solution
L.H.S. = `(sin^2θ)/(cos θ) + cos θ`
= `(sin^2θ + cos^2θ)/(cos θ)`
= `1/(cos θ)` ...[∵ sin2θ + cos2θ = 1]
= sec θ
= R.H.S.
∴ `(sin^2θ)/(cos θ) + cos θ = sec θ`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`(1 + cot^2 theta ) sin^2 theta =1`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
