Advertisements
Advertisements
प्रश्न
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
Advertisements
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)`
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Find the value of sin105°.
Find the value of tan `(7pi)/12`
Prove that sin(π + θ) = − sin θ.
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a product
cos 65° + cos 15°
Express the following as a product
cos 35° – cos 75°
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
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
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
