Advertisements
Advertisements
Question
What is the value of (1 + cot2 θ) sin2 θ?
Advertisements
Solution
We have,
`(1+cot^2 θ)sin^2θ= cosec^2θxxsin^2θ`
`= (1/sinθ)^2 xx sin^2θ`
= `1/sin^2θxxsin^2θ`
`=1`
APPEARS IN
RELATED QUESTIONS
(secA + tanA) (1 − sinA) = ______.
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Find the value of sin 30° + cos 60°.
Find the value of ( sin2 33° + sin2 57°).
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Show that tan4θ + tan2θ = sec4θ – sec2θ.
