Advertisements
Advertisements
Question
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Advertisements
Solution
we know sin2A + cos2A = 1
cos2 A = 1 – sin2A
= `1 - (4/5)^2`
= `1 - 16/25`
= `(25 - 16)/25`
= `9/25`
cos A = `+- sqrt(9/25)`
= `+- 3/5`
Since A lies in the first quadrant, cos A is positive
∴ cos A = `3/5`
cos 2A = cos2A – sin2A
= `(3/5)^2 - (4/5)^2`
= `9/25 - 16/25`
= `(9 - 16)/25`
= `(-7)/25`
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 IV quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Prove that sin 75° – sin 15° = cos 105° + cos 15°
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
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 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
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)
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 A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
