If tan2A = cot (A – 18°), where 2A is an acute angle, then A =

If x = a $cosec\theta cosec\backslash theta$ and y = b $cot\theta cot\backslash theta$, then $b^2{x}^2\text{–}{a}^2{y}^2=b^2x^2\; –\; a^2y^2\; =$

tan 30°, tan 45°, tan 60° are in

$co{s}^4\theta -si{n}^4\theta =cos^4\; \backslash theta-sin^4\backslash theta=$

$sin{0}^{\circ }\mathrm{.}tan60^{\circ }\mathrm{.}cos30^{\circ }\mathrm{.}cosec45^{\circ }=sin\; 0^\backslash circ\; .\; tan\; 60^\backslash circ.\; cos\; 30^\backslash circ.\; cosec\; 45^\backslash circ\; =$

If sin(A + B) = $\frac{1}{\sqrt{2}}\backslash frac\{1\}\{\backslash sqrt2\}$ and cos (A – B) = $\frac{1}{\sqrt{2}}\backslash frac\{1\}\{\backslash sqrt2\}$ then $\mathrm{\angle }B\backslash angle\; B$ =

If sin$\theta \backslash theta$ + cos$\theta \backslash theta$  = $\sqrt{2}\backslash sqrt2$ then $\theta \backslash theta$  =

$\frac{1-ta{n}^{2}30^{\circ }}{1+ta{n}^{2}30^{\circ }}=\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\backslash frac\{1-tan^2\; 30^\backslash circ\}\{1+tan^2\; 30^\backslash circ\}\; =\; .........$

$co{s}^4\theta -si{n}^4\theta =cos^4\; \backslash theta-sin^4\backslash theta=$

If x = cos $\theta \backslash theta$  + sin $\theta \backslash theta$ and y = cos $\theta \backslash theta$ – sin $\theta \backslash theta$, then $x^{2}x^2$ + $y^{2}y^2$ =