Mathematics Tes...

The value of \(81\left(\frac{1}{\log _{5} 3}\right)+27^{\log _{0} 36}+3^{\frac{4}{\log _{7} 9}}\) is equal to

\(\lim _{n \rightarrow \infty} n \cdot \cos \left(\frac{\pi}{4 n}\right) \cdot \sin \left(\frac{\pi}{4 n}\right)\) is equal to

\(\sin ^{-1}|\cos x|-\cos ^{-1}|\sin x|=a\) has at least one solution if \(\mathbf{a} \in\)

\(\lim _{n \rightarrow \infty} \frac{a^{n}+b^{n}}{a^{n}-b^{n}}\) where \(a>b>1,\) is equal to

If \(\int\left(\frac{x-1}{x+1}\right) \frac{d x}{\sqrt{x^{3}+x^{2}+x}}=2 \tan ^{-1} \sqrt{f(x)}+C,\) find \(f(x)\)

The value of \(\sin ^{2} 5^{\circ}+\sin ^{2} 10^{\circ}+\sin ^{2} 15^{\circ}+\ldots \ldots \ldots \ldots \ldots\)

\(\sin ^{2} 85^{\circ}+\sin ^{2} 90^{\circ}\) is equal to

If \(\int \frac{d x}{x \sqrt{1-x^{3}}}=\operatorname{aln}\left(\frac{\sqrt{1-x^{3}}+b}{-\sqrt{1-x^{3}}+1}\right)+k,\) then

\(\int \frac{(2+\sec x) \sec x}{(1+2 \sec x)^{2}} d x\)