Advertisements
Advertisements
प्रश्न
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Advertisements
उत्तर
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
`= 1/2 + 2/1 - (5(1))/(2(1))`
`= 1/2 +2 -5/2`
`= (1+4-5)/2`
`=0/2`
= 0
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.
cot A is the product of cot and A.
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, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
If `sec θ = 13/5`, show that `(2 sin θ - 3 cos θ)/(4 sin θ - 9 cos θ) = 3`.
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
If `sqrt2 sin (60° – α) = 1` then α is ______.
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
If cos A = `4/5`, then the value of tan 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)`
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
