Advertisements
Advertisements
Question
`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`
Solution
LHS= `(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) `
=` ((cos theta + sin theta)(cos^2 theta- cos theta sin theta + sin^2 theta))/((cos theta + sin theta)) + ((cos theta - sin theta )(cos^2 theta+ cos theta sin theta + sin^2 theta))/((cos theta - sin theta))`
=` (cos^2 theta + sin ^2 theta - cos theta sin theta ) + ( cos^2 theta + sin^2 theta + cos theta sin theta)`
=`(1- cos theta sin theta) +( 1+ cos theta sin theta)`
= 2
= RHS
Hence, LHS = RHS
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
(secA + tanA) (1 − sinA) = ______.
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
Simplify : 2 sin30 + 3 tan45.
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
(sec A + tan A) (1 − sin A) = ______.
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
tan θ cosec2 θ – tan θ is equal to
Choose the correct alternative:
tan (90 – θ) = ?
Choose the correct alternative:
Which is not correct formula?
