Advertisements
Advertisements
Question
Show that sin 12° sin 48° sin 54° = `1/8`
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of cos(300°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
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 sin105°.
Prove that sin 105° + cos 105° = cos 45°
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a product
cos 65° + cos 15°
Express the following as a product
sin 50° + sin 40°
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
