Advertisements
Advertisements
प्रश्न
Prove the following:
sin4θ +2sin2θ . cos2θ = 1 − cos4θ
Advertisements
उत्तर
L.H.S. =sin4θ +2sin2θ . cos2θ
= sin2θ(sin2θ + 2cos2θ)
= (sin2θ) (sin2θ + cos2θ + cos2θ)
= (1 – cos2θ) (1 + cos2θ)
= 1 – cos4θ
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
sin 30° + cos 45° + tan 180°
Evaluate the following :
sin 30° × cos 45° × tan 360°
If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`
Eliminate θ from the following:
x = 3secθ , y = 4tanθ
Eliminate θ from the following :
x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ
Eliminate θ from the following:
2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ
Find the acute angle θ such that 2 cos2θ = 3 sin θ.
If cosecθ + cotθ = 5, then evaluate secθ.
If cotθ = `3/4` and π < θ < `(3pi)/2` then find the value of 4cosecθ + 5cosθ.
Prove the following identities:
`(1 + tan^2 "A") + (1 + 1/tan^2"A") = 1/(sin^2 "A" - sin^4"A")`
Prove the following identities:
(sinθ + sec θ)2 + (cosθ + cosec θ)2 = (1 + cosecθ sec θ)2
Prove the following identities:
(1 + cot θ – cosec θ)(1 + tan θ + sec θ) = 2
Prove the following identity:
`tantheta/(sectheta - 1) = (sectheta + 1)/tantheta`
Prove the following identities:
(sec A + cos A)(sec A − cos A) = tan2A + sin2A
Prove the following identity:
1 + 3cosec2θ cot2θ + cot6θ = cosec6θ
Select the correct option from the given alternatives:
`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` is equal to
Select the correct option from the given alternatives:
If cosecθ + cotθ = `5/2`, then the value of tanθ is
Select the correct option from the given alternatives:
`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)` equals
Select the correct option from the given alternatives:
If cosecθ − cotθ = q, then the value of cot θ is
Prove the following:
sin2A cos2B + cos2A sin2B + cos2A cos2B + sin2A sin2B = 1
Prove the following:
`(tan theta + 1/costheta)^2 + (tan theta - 1/costheta)^2 = 2((1 + sin^2theta)/(1 - sin^2theta))`
Prove the following:
sin4θ + cos4θ = 1 – 2 sin2θ cos2θ
Prove the following:
`(sin^3theta + cos^3theta)/(sintheta + costheta) + (sin^3theta - cos^3theta)/(sintheta - costheta)` = 2
Prove the following:
tan2θ − sin2θ = sin4θ sec2θ
Prove the following:
(1 + tanA · tanB)2 + (tanA − tanB)2 = sec2A · sec2B
Prove the following:
`(1 + cottheta + "cosec" theta)/(1 - cottheta + "cosec" theta) = ("cosec" theta + cottheta - 1)/(cottheta - "cosec"theta + 1)`
Prove the following:
`(tantheta + sectheta - 1)/(tantheta + sectheta + 1) = tantheta/(sec theta + 1)`
Prove the following:
`("cosec"theta + cottheta - 1)/( "cosec"theta + cot theta + 1) =(1-sintheta)/costheta`
If 5 tan θ = 4. then `(5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ)` = ______.
