Trigonometric Identities

If $\cos x+{\cos }^{2}x=1$, then what is the value of ${\sin }^{4}x+{\sin }^{2}x$?

What should come in place of ($?$) for the below expression?

$\frac{\sin \left(\theta \right)-\cos \left(\theta \right)+1 }{\sin \left(\theta \right)+\cos \left(\theta \right)-1} =?$

If $\frac{\cos \alpha }{\cos \beta }=\mathrm{m}$ and $\frac{\cos \alpha }{\sin \beta }=\mathrm{n}$, then value of $({\mathrm{m}}^2+{\mathrm{n}}^2) {\cos }^2\beta$_____.

The value of ${\sin }^{2}51°+{\sin }^{2}39°$ is

If $\tan \theta =\frac{a}{b}$, then $\sin \theta =$

If $ABCD$ is a quadrilateral then ${\sec }^2\left(\frac{A+B}{4}\right)-{\cot }^2\left(\frac{C+D}{4}\right)=?$

Find the value of $\frac{1+\tan A}{1+\cot A}$

Simplify: $\frac{1+\tan \mathrm{A}}{1+\cot \mathrm{A}}$

Simplify:

$\frac{se{c}^2\theta -1}{{\tan }^2\theta }=?$

If $\tan \theta =\sqrt{2}-1$ where $\theta$ is an acute angle then the value of $\frac{\sin 2\theta }{2}$ is 

If $\sin \theta +\cos ec\theta =7$, then what is the value of ${\sin }^3\theta +\cos e{c}^3\theta ?$

$se{c}^2\theta -{\tan }^2\theta =1$ is true when/for

For right triangle $ABC$, ${\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C=$___

If $a\cos \theta -b\sin \theta =c$, then $a\sin \theta +b\cos \theta =?$

$\frac{\sin \theta }{1+\cos \theta }$ is

If $3x = \cos ec \theta$ and $\frac{3}{x}= cot\theta$ then the value of $3\left(x^2-\frac{1}{x^2}\right)$ will be ____.

If $\sec \theta +\tan \theta =m$ and $\sec \theta -\tan \theta =n$, then the value of $mn$ is

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

If $5{\sin }^2\theta =3(1+\cos \theta ). 0°<\theta <90°,$ then the value of $\cos ec\theta +cot\theta$ is:

Value of $\sec A(1-\sin A)(\sec A+\tan A)$ is