Advertisements
Advertisements
प्रश्न
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
उत्तर
L.H.S = `(cos("A" + 15^circ))/(sin("A" + 15^circ)) - (sin("A" - 15^circ))/(cos("A" - 15^circ))`
= `(cos("A" + 15^circ)cos("A" - 15^circ) - sin("A" + 15^circ)sin("A" - 15^circ))/(sin("A" + 15^circ) cos("A" - 15^circ))`
= `(cos("A" + 15^circ + "A" - 15^circ))/(1/2[sin("A" + 15^circ + "A" - 15^circ) + sin("A" + 15^circ - "A" + 15^circ)]`
= `(2cos2"A")/(sin2"A" + sin30^circ)`
= `(2cos2"A")/(1/2 + sin2"A")`
= `(4cos2"A")/(1 + 2sin 2"A")`
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of cos 105°.
Find the value of sin 105°
Find the value of tan `(7pi)/12`
Prove that sin(π + θ) = − sin θ.
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Show that tan 75° + cot 75° = 4
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
