Advertisements
Advertisements
प्रश्न
Show that sin 12° sin 48° sin 54° = `1/8`
उत्तर
sin 12° . sin 48° . sin 54° = sin 48° . sin 12° . sin(90° – 36°)
= `1/2` [cos (48° – 12°) – cos (48° + 12°)] cos 36°
= `1/2` [cos 36° – cos 6o°] cos 36°
= `1/2 [cos 36^circ - 1/2] cos 36^circ`
= `1/2 [cos^2 36^circ - 1/2 cos 36^circ]`
= `1/2 [((sqrt(5) + 1)/4)^2 - 1/2((sqrt(5) + 1)/4)]`
= `1/2[(5 + 2sqrt(5) + 1)/16 - ((sqrt(5) + 1)/8)]`
= `1/16 [(5 + 2sqrt(5) + 1)/2 - (sqrt(5) + 1)]`
= `1/16 [(6 + 2sqrt(5) - 2sqrt(5) - 2)/2]`
= `1/16 xx 4/2`
= `1/8`
APPEARS IN
संबंधित प्रश्न
Find the values of sin (– 1110°)
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
Find the value of tan `(7pi)/12`
Show that tan 75° + cot 75° = 4
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
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 sum or difference
cos 5θ cos 2θ
Express the following as a product
sin 50° + sin 40°
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
