Advertisements
Advertisements
Question
Prove that cos(π + θ) = − cos θ
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Find the value of sin105°.
Find the value of tan `(7pi)/12`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin 105° + cos 105° = cos 45°
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a product
sin 50° + sin 40°
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
