Trigonometry Quiz 4

If 5 tan $\alpha$ = 4, then $\frac{5 sin\, \alpha - 3 cos\, \alpha }{5 sin\, \alpha+2 cos\, \alpha } = .......$

$\sqrt{1 + sin^2\, \theta + cos^2\, \theta} = .......$

tan 2A = 1 then A = …………

If x = a sec$\theta$ cos$\phi$, y = b sec$\theta$ sin$\phi$, z = c tan $\theta$, then $\frac{x^2}{a^2} + \frac{y^2}{b^2}$ = ………

If 7$sin^2 \theta$ + 3 $cos^2 \theta$ = 5, then tan $\theta$ = …………

If sin$\theta$ + $sin^2\theta$ = 1, then $cos^2\theta$ + $cos^4\theta$ = …………

If cot$\theta$ + cosec$\theta$  = 5, then cos$\theta$  = ………

$\frac{cos\theta}{1-tan\theta} + \frac{sin\theta}{1-cot\theta}$= ………

If tan$\theta$ = $\frac{7}{8}$ , then the value of $\frac{(1+sin \theta)(1-sin \theta)}{1+cos \theta)(1-cos \theta)}$...........

If cosec$\theta$ + cot$\theta$ = P, then value of cos$\theta$ = …………