Advertisements
Advertisements
Question
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Solution
L.H.S. = (cos A + sin A)2 + (cos A – sin A)2
= cos2 A + sin2 A + 2 cos A . sin A + cos2 A + sin2 A – 2 cos A . sin A
= 2 sin2 A + 2 cos2 A
= 2(sin2 A + cos2 A) ...(∵ sin2 A + cos2 A = 1)
= 2 × 1
= 2
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following trigonometric identities.
`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
`(1 + cot^2 theta ) sin^2 theta =1`
If `sec theta + tan theta = x," find the value of " sec theta`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
