Advertisements
Advertisements
Question
tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to
Options
`4/sqrt3`
`4sqrt3`
1
4
Solution
We have to find `tan 5°xx tan 30° xx4 tan 85°`
We know that
`tan (90°-θ)=cot-θ`
`tan θ cot -θ=1`
`tan 30°=1/sqrt3`
so
`tan 5° xx tan 30° xx 4 tan 85°`
=` tan (90°-85°)xx tan 30°xx4 tan 85°`
= `cot 85° xx tan 30°xx4 tan 85°`
=` 4 cot 85° xx tan 85° tan 30°`
= `4xx1xx1/sqrt3`
= `4/sqrt3`
APPEARS IN
RELATED QUESTIONS
If the angle θ= –60º, find the value of cosθ.
If tan 2θ = cot (θ + 6º), where 2θ and θ + 6º are acute angles, find the value of θ
Prove the following trigonometric identities.
(cosecθ + sinθ) (cosecθ − sinθ) = cot2 θ + cos2θ
Prove the following trigonometric identities.
(secθ + cosθ) (secθ − cosθ) = tan2θ + sin2θ
For triangle ABC, show that : `tan (B + C)/2 = cot A/2`
Evaluate:
`cos70^circ/(sin20^circ) + cos59^circ/(sin31^circ) - 8 sin^2 30^circ`
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
Given
\[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\] what is the value of \[\frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta}\]
If \[\tan \theta = \frac{3}{4}\] then cos2 θ − sin2 θ =
If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x =
Prove the following.
tan4θ + tan2θ = sec4θ - sec2θ
Prove that :
tan5° tan25° tan30° tan65° tan85° = \[\frac{1}{\sqrt{3}}\]
If sin θ =7/25, where θ is an acute angle, find the value of cos θ.
Evaluate: `(cos55°)/(sin 35°) + (cot 35°)/(tan 55°)`
Evaluate: `2(tan57°)/(cot33°) - (cot70°)/(tan20°) - sqrt(2) cos 45°`
Evaluate: 14 sin 30°+ 6 cos 60°- 5 tan 45°.
In the case, given below, find the value of angle A, where 0° ≤ A ≤ 90°.
cos(90° - A) · sec 77° = 1
Solve: 2cos2θ + sin θ - 2 = 0.
Choose the correct alternative:
If ∠A = 30°, then tan 2A = ?
The value of (tan1° tan2° tan3° ... tan89°) is ______.
