Advertisements
Advertisements
Question
If θ = 15°, find the value of: cos3θ - sin6θ + 3sin(5θ + 15°) - 2 tan23θ
Advertisements
Solution
θ = 15°
`(3)/(2)cos3θ - sin6θ + 3sin(5θ + 15°) - 2tan^2 3θ`
= `(3)/(2)cos 3 xx 15° - sin6 xx 15° + 3sin(5 xx 15° + 15°) -2tan^2 3 xx 15°`
= `(3)/(2)cos45° - sin90° + 3sin90° - 2tan^2 45°`
= `(3)/(2) xx (1)/sqrt(2) - 1 + 3 xx 1 - 2 xx (1)^2`
= `(3)/(2sqrt(2)) - 1 + 3 - 2`
= `(3)/(2sqrt(2))`
= `(3)/(2sqrt(2)) xx sqrt(2)/sqrt(2)`
= `(3sqrt(2))/(4)`.
APPEARS IN
RELATED QUESTIONS
If 4 sin2 θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos2 θ + tan2 θ.
If 2 cos 2A = `sqrt3` and A is acute,
find:
(i) A
(ii) sin 3A
(iii) sin2 (75° - A) + cos2 (45° +A)
If 4 cos2 x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x (iv) sin 2x
Solve the following equation for A, if 2cos2A = 1
Find the magnitude of angle A, if 2 tan 3A cos 3A - tan 3A + 1 = 2 cos 3A
Find the value of 'A', if 2 sin 2A = 1
Find lengths of diagonals AC and BD. Given AB = 24 cm and ∠BAD = 60°.
In the given figure, if tan θ = `(5)/(13), tan α = (3)/(5)` and RS = 12m, find the value of 'h'.
Evaluate the following: `(sin62°)/(cos28°)`
Prove the following: `(tan(90° - θ)cotθ)/("cosec"^2 θ)` = cos2θ
