Advertisements
Advertisements
प्रश्न
If cos A = `4/5`, then the value of tan A is ______.
पर्याय
`3/5`
`3/4`
`4/3`
`5/3`
`1/8`
Advertisements
उत्तर
If cos A = `4/5`, then the value of tan A is `underlinebb(3/4)`.
Explanation:
According to the question,
cos A = `4/5` ...(1)
We know,
tan A = `(sin A)/(cos A)`
To find the value of sin A,
We have the equation,
sin2θ + cos2θ = 1
So, sin θ = `sqrt(1 - cos^2θ)`
Then,
sin A = `sqrt(1 - cos^2A)` ...(2)
sin2A = 1 – cos2A
sin A = `sqrt(1 - cos^2A)`
Substituting equation (1) in (2),
We get,
sin A = `sqrt(1 - (4/5)^2)`
= `sqrt(1 - (16/25))`
= `sqrt(9/25)`
= `3/4`
Therefore, tan A = `3/5 xx 5/4 = 3/4`
संबंधित प्रश्न
Given sec θ = `13/12`, calculate all other trigonometric ratios.
In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of
- sin A cos C + cos A sin C
- cos A cos C − sin A sin C
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Evaluate the Following:
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
