Advertisements
Advertisements
प्रश्न
Prove the following:
2 sec2θ – sec4θ – 2cosec2θ + cosec4θ = cot4θ – tan4θ
Advertisements
उत्तर
L.H.S. = 2 sec2θ – sec4θ – 2cosec2θ + cosec4θ
= 2 sec2θ – (sec2θ)2 – 2cosec2θ + (cosec2θ)2
= 2(1 + tan2θ) – (1 + tan2θ)2 – 2(1 + cot2θ) + (1 + cot2θ)2
= 2 + 2tan2θ – (1 + 2tan2θ + tan4θ) – 2 – 2cot2θ + 1 + 2cot2θ + cot4θ
= 2 + 2tan2θ – 1 – 2tan2θ – tan4θ – 2 – 2cot2θ + 1 + 2cot2θ + cot4θ
= cot4θ – tan4θ
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
sin 30° + cos 45° + tan 180°
Evaluate the following :
cosec 45° + cot 45° + tan 0°
Evaluate the following :
sin 30° × cos 45° × tan 360°
Eliminate θ from the following :
x = 6cosecθ, y = 8cotθ
Eliminate θ from the following :
x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ
Eliminate θ from the following :
x = 5 + 6cosecθ, y = 3 + 8cotθ
Find sinθ such that 3cosθ + 4sinθ = 4
If cotθ = `3/4` and π < θ < `(3pi)/2` then find the value of 4cosecθ + 5cosθ.
Prove the following identities:
(cos2A – 1) (cot2A + 1) = −1
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:
`1/(sectheta + tantheta) - 1/costheta = 1/costheta - 1/(sectheta - tantheta)`
Prove the following identity:
`tantheta/(sectheta - 1) = (sectheta + 1)/tantheta`
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
Prove the following identity:
1 + 3cosec2θ cot2θ + cot6θ = cosec6θ
Prove the following identities:
`(1 - sectheta + tan theta)/(1 + sec theta - tan theta) = (sectheta + tantheta - 1)/(sectheta + tantheta + 1)`
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:
If cosecθ − cotθ = q, then the value of cot θ is
Select the correct option from the given alternatives:
The value of tan1°.tan2°tan3°..... tan89° is equal to
Prove the following:
`(tan theta + 1/costheta)^2 + (tan theta - 1/costheta)^2 = 2((1 + sin^2theta)/(1 - sin^2theta))`
Prove the following:
cos4θ − sin4θ +1= 2cos2θ
Prove the following:
sin4θ +2sin2θ . cos2θ = 1 − cos4θ
Prove the following:
tan2θ − sin2θ = sin4θ sec2θ
Prove the following:
(sinθ + cosecθ)2 + (cosθ + secθ)2 = tan2θ + cot2θ + 7
Prove the following:
sin8θ − cos8θ = (sin2θ − cos2θ) (1 − 2 sin2θ cos2θ)
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`
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 ______.
