Advertisements
Advertisements
Question
If 0° < A < 90°; find A, if `(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
Advertisements
Solution
`(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
`=> (cos A + cos A sin A + cos A - sin A cos A)/((1 - sin A)(1 + sin A)) = 4`
`=> (2 cos A)/(1 - sin^2 A) = 4`
`=> (2 cos A)/(cos^2 A) = 4`
`=> 1/cos A = 2`
`=> cos A = 1/2`
We know `cos 60^circ = 1/2`
Hence, A = 60°
RELATED QUESTIONS
Solve.
`tan47/cot43`
Show that : `sin26^circ/sec64^circ + cos26^circ/(cosec64^circ) = 1`
Evaluate:
14 sin 30° + 6 cos 60° – 5 tan 45°
Use tables to find the acute angle θ, if the value of tan θ is 0.2419
Evaluate:
cos 40° cosec 50° + sin 50° sec 40°
If \[\tan \theta = \frac{1}{\sqrt{7}}, \text{ then } \frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta} =\]
If \[\tan \theta = \frac{3}{4}\] then cos2 θ − sin2 θ =
Prove that:
\[\frac{sin\theta \cos(90° - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]
Evaluate: 14 sin 30°+ 6 cos 60°- 5 tan 45°.
If sin A = `3/5` then show that 4 tan A + 3 sin A = 6 cos A
