Advertisements
Advertisements
प्रश्न
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Advertisements
उत्तर
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
संबंधित प्रश्न
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
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.
`cos A = 4/5`
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(∵ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
Find will be the value of cos 90° + sin 90°.
If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to ______.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
