Advertisements
Advertisements
प्रश्न
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Advertisements
उत्तर
tan2 30° + tan2 60° + tan2 45° ....(i)
By trigonometric ratios we have
`tan 30^@ = 1/sqrt3 tan 60^@ = sqrt3 tan 45^@ = 1`
By substituting above values in (i), we get
`[1/sqrt3]^2 + [sqrt3]^2 + [1]^2`
`=> 1/3 + 3 + 1 => 1/3 + 4`
`=> (1 + 12)/3 = 13/3`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
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.
cot A is the product of cot and 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.
`sin A = 2/3`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
If `sqrt2 sin (60° – α) = 1` then α is ______.
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.
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 θ is an acute angle of a right angled triangle, then which of the following equation is not true?
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
