Mathematics Tes...

If \(a, b,\) care positive, then \(\sum \tan ^{-1} \sqrt{\frac{a(a+b+c)}{b c}}=\)

If tan 45° + cosec 30° = x, then find the value of x

Find the principle value of cos⁻¹−(1/√2)

The principal value of \(\tan ^{-1}\left(\cot \frac{3 \pi}{4}\right)\) is :

The number of triplets (x,y,z), where x,y,z∈[0,2π], satisfying the inequality

(1+cos⁴x)(2+cot²y)(4+sin4z)≤12cos²x are

If \(\tan ^{-1} \frac{\sqrt{1+x^{2}}-1}{x}=4^{\circ},\) then

Number of solutions of the equation \(\cot ^{-1}\left(\frac{x^{2}-1}{2 x}\right)+\tan ^{-1}\left(\frac{2 x}{x^{2}-1}\right)=\frac{2 \pi}{3}\) are

If \(\cos ^{-1} \sqrt{p}+\cos ^{-1} \sqrt{1-p}+\cos ^{-1} \sqrt{1-q}=\frac{3 \pi}{4},\) then the value of \(q\) is

\(\mathrm{f} \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)=K, \forall x \in[-1,0],\) then the value of \(\mathrm{K}\) is

\(\lim _{x \rightarrow 1}\left[\sec \left(\frac{\pi x}{2}\right) \log x\right]\) is: