Advertisements
Advertisements
प्रश्न
Prove that cos(π + θ) = − cos θ
उत्तर
L..H.S = cos(π + θ)
= cos(180° + θ)
= cos 180° cos θ – sin 180° sin θ
= (– 1) cos θ – (0) sin θ
= – cos θ
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of `sin (-(11pi)/3)`
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
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 the value of cos 105°.
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Express the following as a sum or difference
2 sin 10θ cos 2θ
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 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 `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
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) =
