Advertisements
Advertisements
Question
If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ −\[\sqrt{3} \tan 3\theta\] is equal to
Options
1
0
−1
\[1 + \sqrt{3}\]
Solution
We are given that 5θ and 4θ are acute angles satisfying the following condition sin 5θ = cos 4θ. We are asked to find 2 `sin 3θ -sqrt3 tan 3θ `
⇒ `sin 5θ= cos 4θ`
⇒` cos (90°-5θ)= cos 4θ`
⇒` 90°-5θ=4θ`
⇒ `90=90°`
Where `5θ` and `4θ` are acute angles
⇒ `θ=10°`
Now we have to find:
`2 sin 3θ-sqrt3 tan 3θ`
=` 2 sin 30°-sqrt3 tan 30°`
= `2xx1/2-sqrt3xx1/sqrt3`
=`1-1`
=` 0`
APPEARS IN
RELATED QUESTIONS
If sin θ =3/5, where θ is an acute angle, find the value of cos θ.
If the angle θ = -60° , find the value of sinθ .
Evaluate cosec 31° − sec 59°
Without using trigonometric tables evaluate:
`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`
Prove the following trigonometric identities.
(cosecA − sinA) (secA − cosA) (tanA + cotA) = 1
Solve.
`cos22/sin68`
Express the following in terms of angles between 0° and 45°:
cos74° + sec67°
Evaluate:
tan(55° - A) - cot(35° + A)
Use tables to find cosine of 26° 32’
Use tables to find the acute angle θ, if the value of tan θ is 0.7391
If \[\tan \theta = \frac{4}{5}\] find the value of \[\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta}\]
If A + B = 90° and \[\tan A = \frac{3}{4}\]\[\tan A = \frac{3}{4}\] what is cot B?
If 5 tan θ − 4 = 0, then the value of \[\frac{5 \sin \theta - 4 \cos \theta}{5 \sin \theta + 4 \cos \theta}\] is:
If A and B are complementary angles, then
If angles A, B, C to a ∆ABC from an increasing AP, then sin B =
If \[\cos \theta = \frac{2}{3}\] then 2 sec2 θ + 2 tan2 θ − 7 is equal to
Without using trigonometric tables, prove that:
sec70° sin20° + cos20° cosec70° = 2
A, B and C are interior angles of a triangle ABC. Show that
If ∠A = 90°, then find the value of tan`(("B+C")/2)`
Express the following in term of angles between 0° and 45° :
sin 59° + tan 63°
Evaluate: `2(tan57°)/(cot33°) - (cot70°)/(tan20°) - sqrt(2) cos 45°`
