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 :
cosec 45° + cot 45° + tan 0°
If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`
Eliminate θ from the following :
x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ
Eliminate θ from the following :
x = 5 + 6cosecθ, y = 3 + 8cotθ
Eliminate θ from the following:
2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ
Find the acute angle θ such that 5tan2θ + 3 = 9secθ.
Find sinθ such that 3cosθ + 4sinθ = 4
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:
`1/(sectheta + tantheta) - 1/costheta = 1/costheta - 1/(sectheta - tantheta)`
Prove the following identities:
`sintheta/(1 + costheta) + (1 + costheta)/sintheta` = 2cosecθ
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 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:
`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` 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:
sin2A cos2B + cos2A sin2B + cos2A cos2B + sin2A sin2B = 1
Prove the following:
`((1 + cot theta + tan theta)(sin theta - costheta)) /(sec^3theta - "cosec"^3theta)`= sin2θ cos2θ
Prove the following:
sin4θ + cos4θ = 1 – 2 sin2θ cos2θ
Prove the following:
2(sin6θ + cos6θ) – 3(sin4θ + cos4θ) + 1 = 0
Prove the following:
cos4θ − sin4θ +1= 2cos2θ
Prove the following:
`(sin^3theta + cos^3theta)/(sintheta + costheta) + (sin^3theta - cos^3theta)/(sintheta - costheta)` = 2
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:
`("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)`
