Home
Class 12
MATHS
Simplify [(3sin2alpha)/(5+3cos2alpha)]+t...

Simplify `[(3sin2alpha)/(5+3cos2alpha)]+tan^(-1)[(tanalpha)/4],w h e r e-pi/2

Text Solution

AI Generated Solution

To simplify the expression \[ \frac{3 \sin 2\alpha}{5 + 3 \cos 2\alpha} + \tan^{-1}\left(\frac{\tan \alpha}{4}\right) \] where \(-\frac{\pi}{2} < \alpha < \frac{\pi}{2}\), we will follow these steps: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Simplify [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alpha)/(4)], " where " -(pi)/(2) lt alpha lt (pi)/(2)

Simplify tan^-1[(3 sin 2alpha)/(5+3 cos2 alpha)]+tan^(-1)[(tan alpha)/4]

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

the expression (1+sin2alpha)/(cos(2alpha-2pi)tan(alpha-(3pi)/4))-1/4sin2alpha(cot(alpha/2)+cot((3pi)/2+alpha/2)) simplifies and reduces to

If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e n tan(pi/4- u/2) is (a) sqrt(tanalpha) (b) sqrt(cotalpha) (c) tanalpha (d) cot alpha

Solve: sin3alpha=4sinalphasin(x+alpha)sin(x-alpha),w h e r ealpha!=npi,n in Z

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

tanalpha.tan(60^@-alpha).tan(60^@+alpha)=tan3alpha

If (2 sin alpha)/(1 + cos alpha + sin alpha) = 3/4 , then the value of (1 - cos alpha + sinalpha)/(1 + sin alpha) is equal to

If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4, u/2)i se q u a lto (a) sqrt(tanalpha) (b) sqrt(cotalpha) (c) tanalpha (d) cot alpha