Advertisements
Advertisements
प्रश्न
Prove that sin 105° + cos 105° = cos 45°
उत्तर
sin 105° + cos 105° = sin(90° + 15°) + cos(90° + 15°)
= cos 15° – sin 15°
= cos(45° – 30°) sin(45° – 30°)
= (cos 45° . cos30° + sin 45° sin 30°) – (sin 45° cos 30° – cos 45° sin 30°)
= `(1/sqrt(2) * sqrt(3)/2 + 1/sqrt(2) * 1/sqrt(2)) - (1/sqrt(2) * sqrt(3)/2 - 1/sqrt(2) * 1/sqrt(2))`
= `sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2)) - sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2))`
= `2/(2sqrt(2))`
= `1/sqrt(2)`
= cos 45°
APPEARS IN
संबंधित प्रश्न
Find the values of `sin (-(11pi)/3)`
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
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
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 cos 105°.
Find the value of sin 105°
Prove that cos(π + θ) = − cos θ
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
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
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
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 sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
