Advertisements
Advertisements
प्रश्न
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Advertisements
उत्तर
`cot^2 30^circ - 2 cos^2 60^circ - 3/4 sec^2 45^@ - 4 sec^2 30^circ`
By trigonometric ratios we have
`cot 30^@ = sqrt3 cos 60^@ = 1/2 sec 45^@ = sqrt2 sec 30^@ = 2/sqrt3`
By trigonometric ratios we have
`(sqrt3)^2 - 2[1/2]^2 - 3/4 (sqrt2)^2 - 4[2/sqrt3]^2`
`3 - 2 xx 1/4 - 3/4 xx 2 - 4 xx 4/3`
= `3/1 - 1/2 - 3/2 - 16/3`
= `(18 - 3 - 9 - 32)/6`
= `(18 - 44)/6`
= `(-26)/6`
= `(-13)/3`
APPEARS IN
संबंधित प्रश्न
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
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
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Find the value of x in the following :
`2 sin x/2 = 1`
`(sin theta)/(1 + cos theta)` is ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
5 tan² A – 5 sec² A + 1 is equal to ______.
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Find the value of sin 45° + cos 45° + tan 45°.
In the given figure, if sin θ = `7/13`, which angle will be 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 ______.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
