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
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that cot2θ × sec2θ = cot2θ + 1
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
(1 + sin A)(1 – sin A) is equal to ______.
