Inverse Trigono...

If $$x$$ takes negative permissible value, then  $$\sin^{-1}x=$$

There is flag-staff at the top of $$10$$ metres high tower. lf the flag-staff makes an angle $$\tan ^{ -1 }{ \left( 1/8 \right)  }$$ at a point $$24$$ metres away from the tower, then the height of the flag staff in metres is

If $$\tan(cos^{-1}x)=\sin (\sec^{-1} (\sqrt{5}) )$$, then $$x=$$

A tower stands at the top of a hill whose height is three times the height of the tower. The tower is found to subtend an angle of\$$\tan ^{ -1 }{ \left( { 1 }/{ 7 } \right)  } $$ at a point $$2km$$ away on the horizontal throught the foot of the hill. Then the height of the tower is

If $$\theta = sin^{-1}x+cos^{-1}x+tan^{-1}x,\ 0\leq x\leq 1$$, then the smallest interval in which $$\theta$$ lies is given by

The domain of $$\sin^{-1}[\log_{2}(x^{2}/2)]$$ is

$$A$$ vertical pole subtends an angle $$\displaystyle \tan^{-1}(\frac{1}{2})$$ at a point $$P$$ on the ground. The angle subtended by the upper half of the pole at $$P$$ is

Range of $$\sin^{-1}x-\cos^{-1}x$$ is

$$ABC$$ is a triangular park with $$AB=AC=100$$ cm. $$A$$ clock tower is situated at the midpoint of $$BC$$. The angles of elevation of the top of the tower from $$A$$ and $$B$$ are $$cot ^{-1}3.2$$ and $$cosec ^{-1} 2.6$$. The height of the tower is

A vertical pole more than $$100ft$$ high consists of two portions, the lower being $$ 1/3$$ of the whole. lf the upper portion subtends an angle $$\tan^{-1}(1/2)$$ at a point distant 40 ft. from the foot of the pole, the height of the pole is