Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
3
2
1
0
उत्तर
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 2.
Explanation:
Given 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`
= `(sin^2 22^circ + sin^2(90^circ - 22^circ))/(cos^2(90^circ - 68^circ) + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin(90^circ - 63^circ)`
= `(sin^2 22^circ + cos^2 22^circ)/(sin^2 68^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ * cos 63^circ` ...`[(∵ sin(90^circ - theta) = cos theta),("and" cos(90^circ - theta) = sin theta)]`
= `1/1 + (sin^2 63^circ + cos^2 63^circ)` ...[∵ sin2θ + cos2θ = 1]
= 1 + 1
= 2
APPEARS IN
संबंधित प्रश्न
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
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
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°.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ 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.
