Advertisements
Advertisements
प्रश्न
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Advertisements
उत्तर
sin(30° + θ) + cos(60° + θ) = cos θ
sin(30° + θ) + cos(60° + θ)
= sin 30° cos θ + cos 30° sin θ + cos 60° cos θ – sin 60° sin θ
= `1/2 cos theta + sqrt(3)/2 sin theta + 1/2 cos theta - sqrt(3)/2 sin theta`
= cos θ
APPEARS IN
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV 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)
Find the value of cos 105°.
Prove that sin 105° + cos 105° = cos 45°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
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 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
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 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
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
