Advertisements
Advertisements
प्रश्न
Express the following as a product
sin 75° sin 35°
Advertisements
उत्तर
We know sin C – sin D = `2 cos ("C" + "D")/2 * sin ("C" - "D")/2`
Take C = 75°, D = 35°
sin 75° – sin 35° = `2cos((75^circ + 35^circ)/2) * sin((75^circ - 35^circ)/2)`
sin 75° – sin 35° = `2cos(110^circ/2) * sin(40^circ/2)`
sin 75° – sin 35° = 2 cos 55° sin 20°
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of tan(1050°)
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
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)
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 cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
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 sin A = `4/5`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
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)`
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
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) =
