Advertisements
Advertisements
प्रश्न
Express the following as a product
cos 65° + cos 15°
Advertisements
उत्तर
We know sin C – sin D = `2 cos ("C" + "D")/2 * cos ("C" - "D")/2`
Take C = 65°, D = 15°
cos 65° + cos 15° = `2cos((65^circ + 15^circ)/2) * cos((65^circ - 15^circ)/2)`
cos 65° + cos 15° = `2cos(80^circ/2) * cos(50^circ/2)`
cos 65° + cos 15° = 2 cos 40° . cos 25°
APPEARS IN
संबंधित प्रश्न
Find the values of cos(300°)
Find the values of tan(1050°)
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
Find the value of sin105°.
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
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)`
Express the following as a sum or difference
sin 5θ sin 4θ
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
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)
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
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) =
