Advertisements
Advertisements
प्रश्न
If sin A = `1/2`, then the value of cot A is ______.
विकल्प
`sqrt(3)`
`1/sqrt(3)`
`sqrt(3)/2`
1
Advertisements
उत्तर
If sin A = `1/2`, then the value of cot A is `underlinebb(sqrt(3))`.
Explanation:
According to the question,
sin A = `1/2` ...(1)
We know that,
cot A = `1/(tan A) = (cos A)/(sin A)` ...(2)
To find the value of cos A.
We have the equation,
sin2 θ + cos2 θ = 1
So, cos θ = `sqrt(1 - sin^2θ)`
Then,
cos A = `sqrt(1 - sin^2A)` ...(3)
cos2A = 1 – sin2A
cos A = `sqrt(1 - sin^2A)`
Substituting equation 1 in 3, we get,
cos A = `sqrt(1 - 1/4)`
= `sqrt(3/4)`
= `sqrt(3)/2`
Substituting values of sin A and cos A in equation 2, we get
cot A = `(sqrt(3)/2) xx 2`
= `sqrt(3)`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
Given sec θ = `13/12`, calculate all other trigonometric ratios.
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
If `tan theta = 24/7`, find that sin 𝜃 + cos 𝜃
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Find the value of x in the following :
`sqrt3 sin x = cos x`
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
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°.
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
