Advertisements
Advertisements
Question
Find A, if 0° ≤ A ≤ 90° and 2 cos2 A + cos A – 1 = 0
Advertisements
Solution
2 cos2 A + cos A – 1 = 0
`=>` 2 cos2 A + 2 cos A – cos A – 1 = 0
`=>` 2 cos A (cos A + 1) – 1(cos A + 1) = 0
`=>` (2 cos A – 1)(cos A + 1) = 0
`=>` cos A = `1/2` or cos A = –1
We know `cos 60^circ = 1/2`
We also know that for no value of A(0° ≤ A ≤ 90°), cos A = –1.
Hence, A = 60°
APPEARS IN
RELATED QUESTIONS
Evaluate `(sin 18^@)/(cos 72^@)`
Prove the following trigonometric identities.
(cosecθ + sinθ) (cosecθ − sinθ) = cot2 θ + cos2θ
if `tan theta = 1/sqrt2` find the value of `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + cot^2 theta)`
Use tables to find the acute angle θ, if the value of tan θ is 0.4741
If A and B are complementary angles, prove that:
cot A cot B – sin A cos B – cos A sin B = 0
If ∆ABC is right angled at C, then the value of cos (A + B) is ______.
Express the following in term of angles between 0° and 45° :
cosec 68° + cot 72°
Evaluate: `(sin 80°)/(cos 10°)`+ sin 59° sec 31°
Evaluate: 14 sin 30°+ 6 cos 60°- 5 tan 45°.
If x and y are complementary angles, then ______.
