Advertisements
Advertisements
Question
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Options
−1
1
0
None of these
Advertisements
Solution
Given:
`sin θ+sin^2θ=1`
`⇒ 1-sin^2θ= sin θ`
Now,
`cos^2θ+cos^4θ`
`= cos^2 θ+cos^2θcos^2θ`
=` cos^2θ+(1-sin^2θ)(1-sin^2θ)`
`=cos^2θ+sinθ sinθ`
`=cos^2 θ+sin^2θ`
`=1`
APPEARS IN
RELATED QUESTIONS
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Find A if tan 2A = cot (A-24°).
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
