List of top Mathematics Questions on Trigonometry asked in NIMCET

Consider graph of function \(f(x)=2\cos\left(\frac{x}{2}\right)+3\), \(g(x)=4\). The number of points of intersection of two graphs in interval \([0,4\pi]\) is:

Let \(x-y\tan35^\circ=\tan25^\circ(y+x\tan35^\circ)\) for some \(x,y\in\mathbb{R}\). Then which of the following is true?

An engineer standing at point \(P\) wishes to determine the width of a rectangular pond. She finds distance to westernmost point \(A\) to be \(60\) m and distance to northernmost point \(B\) to be \(80\) m. If angle \(APB=60^\circ\), find \(AB\).

\(BC=a,\; AC=b,\; AB=c\) are sides of \(\triangle ABC\) and \(\angle C\neq \frac{\pi}{2}\). Which of the following is not correct?

If \[ \tan^{-1}(3x)+\tan^{-1}(2x)=\frac{\pi}{4}, \] then find the value of \(x\):

From top of view point at height of \(80\,\text{m}\), the angles of depression of the top and bottom of a flag standing on the same plane are observed to be \(30^\circ\) and \(45^\circ\). Find the height of the flag.

Given \[ \cos6x=(a)\cos^6x+(b)\cos^4x+(c)\cos^2x+(d) \] for any real number \(x\), where \(a,b,c,d\) are constants. Find the value of \(a+b+c\).

The value of \(\cos^{-1}\left(\cos\left(-\frac{\pi}{6}\right)\right)+\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)\) is:

The maximum value of \(\sin x+\sin(x+1)\) is \(k\cos\frac12\). Find \(k\).

If the equation \(\cos^4\theta+\sin^4\theta+\lambda=0\) has real solutions, then \(\lambda\) lies in which interval?