Advertisements
Advertisements
Question
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Advertisements
Solution
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@` .....(i)
By trigonometric ratios we have
`cot 30^@ = sqrt3 sin 60^@ = sqrt3/2 cos 45^@ = 1/sqrt2`
By substituting above values in (i), we get
`4/(sqrt3)^2 + 1/(sqrt3/2)^2 - (1/sqrt2)^2`
`4/3 + 4/3 - 1/2 = 13/6`
APPEARS IN
RELATED QUESTIONS
Given sec θ = `13/12`, calculate all other trigonometric ratios.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `sec θ = 13/5`, show that `(2 sin θ - 3 cos θ)/(4 sin θ - 9 cos θ) = 3`.
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If cos A + cos² A = 1, then sin² A + sin4 A 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`
The value of the expression (sin 80° – cos 80°) is negative.
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
What will be the value of sin 45° + `1/sqrt(2)`?
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
