Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cos2A – 1) (cot2A + 1) = −1
Advertisements
उत्तर
L.H.S. = (cos2A – 1) (cot2A + 1)
= – (1 – cos2A)(1 + cot2A)
= – sin2A · cosec2A
= `- sin^2"A" xx 1/sin^2"A"`
= – 1
= R.H.S.
APPEARS IN
संबंधित प्रश्न
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 = 6cosecθ, y = 8cotθ
Find the acute angle θ such that 5tan2θ + 3 = 9secθ.
If cosecθ + cotθ = 5, then evaluate secθ.
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 identities:
`tan^3theta/(1 + tan^2theta) + cot^3theta/(1 + cot^2theta` = secθ cosecθ – 2sinθ cosθ
Prove the following identities:
`1/(sectheta + tantheta) - 1/costheta = 1/costheta - 1/(sectheta - tantheta)`
Prove the following identities:
`sintheta/(1 + costheta) + (1 + costheta)/sintheta` = 2cosecθ
Prove the following identities:
`cottheta/("cosec" theta - 1) = ("cosec" theta + 1)/cot theta`
Prove the following identities:
(sec A + cos A)(sec A − cos A) = tan2A + sin2A
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 θ = 60°, then `(1 + tan^2theta)/(2tantheta)` is equal to
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:
The value of tan1°.tan2°tan3°..... tan89° is equal to
Prove the following:
2(sin6θ + cos6θ) – 3(sin4θ + cos4θ) + 1 = 0
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:
(sinθ + cosecθ)2 + (cosθ + secθ)2 = tan2θ + cot2θ + 7
Prove the following:
sin6A + cos6A = 1 − 3sin2A + 3 sin4A
Prove the following:
(1 + tanA · tanB)2 + (tanA − tanB)2 = sec2A · sec2B
Prove the following:
`("cosec"theta + cottheta - 1)/( "cosec"theta + cot theta + 1) =(1-sintheta)/costheta`
Prove the following identity:
`(1 - sec theta + tan theta)/(1 + sec theta - tan theta) = (sec theta + tan theta - 1)/(sec theta + tan theta + 1)`
If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to ______.
