Advertisements
Advertisements
Question
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Advertisements
Solution
Given,
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°) …(i)
= `((sqrt2)^2 · (2/sqrt3)^2)((1/2)^2 + 4(1)^2 - (2)^2)`
= `(8/3)(1/4 + 4 - 4)`
= `8/3·1/4`
= `2/3`
APPEARS IN
RELATED QUESTIONS
If sin A = `3/4`, calculate cos A and tan A.
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If cos (40° + A) = sin 30°, then value of A is ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.
The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
In the given figure, if sin θ = `7/13`, which angle will be θ?
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
If cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
