Advertisements
Advertisements
प्रश्न
Prove that sin 105° + cos 105° = cos 45°
Advertisements
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 (– 1110°)
Find the values of `sin (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Prove that sin(π + θ) = − sin θ.
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Express the following as a product
sin 50° + sin 40°
Express the following as a product
cos 35° – cos 75°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
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 sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
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 ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
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) =
