Advertisements
Advertisements
प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
उत्तर
L.H.S. = `(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)`
= `((cos27^circ)/(cos27^circ) + (sin27^circ)/(cos27^circ))/((cos27^circ)/(cos27^circ) - (sin27^circ)/(cos27^circ))`
= `(1 + tan27^circ)/(1 - tan27^circ)`
= `(tan45^circ + tan27^circ)/(1 - tan45^circ xx tan27^circ)` ...[∵ tan45° = 1]
= tan(45° + 27°)
= tan72°
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
(cos x + cos y)2 + (sin x – sin y)2 = `4cos^2 ((x + y))/2`
Prove the following:
(cos x – cos y)2 + (sin x – sin y)2 = `4sin^2 ((x - y))/2`
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:
`(2cos 4x + 1)/(2cosx + 1)` = (2 cos x – 1) (2 cos 2x – 1)
Prove the following:
cos2x + cos2(x + 120°) + cos2(x – 120°) = `3/2`
Prove the following:
`4 cos x. cos(x + pi/3) . cos (x - pi/3)` = cos 3x
Prove the following:
`sinx tan(x/2) + 2cosx = 2/(1 + tan^2(x/2))`
Select the correct option from the given alternatives :
The value of cos A cos (60° – A) cos (60° + A) is equal to ......
Select the correct option from the given alternatives :
The value of `sin pi/14sin (3pi)/14sin (5pi)/14sin (7pi)/14sin (9pi)/14sin (11pi)/14sin (13pi)/14` is ....
Prove the following:
`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`
`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 ______.
If `x + 1/x` = 2 cos θ, then `x^n + 1/x^n` is equal to ______.
`(1 - tan^2(45^circ - A))/(1 + tan^2(45^circ - A))` is equal to ______.
If cos 2α = `(3 cos 2β - 1)/(3 - cos 2β)`, then tan α 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 ______.
The value of `(cos^3θ - cos 3θ)/cosθ + (sin^3θ + sin 3θ)/sinθ` is ______.
`(sin(90^circ - θ) sin θ)/tanθ + sin^2 θ` is equal to ______.
If sin θ = `1/2` and θ is acute, then (3 cos θ – 4 cos3 θ) is equal to ______.
If `tan x + tan(π/3 - x) tan ((2π)/3 + x)` = 3, then ______.
If x sin θ = y cos θ = `(2z tan θ)/(1 - tan^2 θ)`, then 4z2(x2 + y2) is equal to ______.
`(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` = ______.
(sec 2A + 1) sec2 A = ______.
2 sin A cos3 A – 2 sin3 A cos A = ______.
The value of sin 3A sin3 A + cos 3A cos3 A is ______.
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to ______.
