Advertisements
Advertisements
प्रश्न
Prove the following:
2cosec 2x + cosec x = `secx cot(x/2)`
उत्तर
L.H.S. = 2cosec 2x + cosec x
= `2/(sin2x) + 1/sinx`
= `2/(2sin x cosx) + 1/sinx`
= `1/(sinx cosx) + 1/sinx`
= `(1 + cosx)/(sinx cosx)`
= `(2cos^2(x/2))/([2sin(x/2)cos(x/2)]cosx`
= `1/cosx * (cos(x/2))/(sin(x/2)`
= `sec x cot (x/2)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
Prove the following:
tan10° + tan35° + tan10°.tan35° = 1
Prove the following:
(sin 3x + sin x)sin x + (cos 3x – cos x) cos x = 0
Prove the following:
`cosx/(1 + sinx) = (cot(x/2) - 1)/(cot(x/2) + 1)`
Prove the following:
`(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` = secθ
Prove the following:
cos7° cos 14° cos28° cos 56° = `sin68^circ/(16cos83^circ)`
Prove the following:
`4 cos x. cos(x + pi/3) . cos (x - pi/3)` = cos 3x
Select the correct option from the given alternatives :
If α + β + γ = π then the value of sin2α + sin2β – sin2γ is equal to …......
Prove the following:
`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`
Prove the following:
`(sin5x - 2sin3x + sinx)/(cos5x - cosx)` = tanx
Prove the following:
cot4x (sin5x + sin3x) = cotx (sin5x − sin3x)
Prove the following:
`sqrt(3) "cosec"20^circ - sec20^circ` = 4
cos4 θ – sin4 θ is equal to ______.
`sqrt(3) "cosec" 20^circ - sec 20^circ` is equal to ______.
Let α and β be such that π < α – β < 3π. If sin α + sin β = `- 21/65` and cos α + cos β = `-27/65`, then the value of `cos ((α - β))/2` is ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If tan A and tan B are the roots of x2 – ax + b = 0, then the value of sin2(A + B) is ______.
For any angle θ, the expression `(2 cos 8θ + 1)/(2 cos θ + 1)` is equal to ______.
`(sin(90^circ - θ) sin θ)/tanθ + sin^2 θ` is equal to ______.
If θ is acute and `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3, then θ is equal to ______.
If `tan x + tan(π/3 - x) tan ((2π)/3 + x)` = 3, then ______.
`(sin θ + sin 2θ)/(1 + cos θ + cos 2θ)` = ______.
If tan α = `1/7`, tan β = `1/3`, then cos 2α = ______.
If tan β = cos θ tan α, then `tan^2 θ/2` = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The value of `sin π/10` is ______.
The value of sin 3A sin3 A + cos 3A cos3 A is ______.
