Advertisements
Advertisements
प्रश्न
Express the following as a product
cos 65° + cos 15°
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
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 cos 105°.
Find the value of sin 105°
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
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)`
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
sin 4x cos 2x
Express the following as a product
sin 75° sin 35°
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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 cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
