NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications

Exercise 8.2

\(\dfrac{\tan 47^\circ}{\cot 43^\circ}=1\). Write ‘True’ or ‘False’ and justify.

The value of the expression \(\cos^2 23^\circ-\sin^2 67^\circ\) is positive.

The value of the expression \(\sin 80^\circ-\cos 80^\circ\) is negative.

\(\sqrt{1-\cos^2\theta}\;\sec^2\theta=\tan\theta\).

If \(\cos A+\cos^2A=1\), then \(\sin^2A+\sin^4A=1\).

\((\tan\theta+2)(2\tan\theta+1)=5\tan\theta+\sec^2\theta\).

If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.

A man 3 m above the surface of a lake observes a cloud and its reflection in the lake. The angle of elevation of the cloud equals the angle of depression of its reflection.

The value of \(2\sin\theta\) can be \(a+\dfrac{1}{a}\), where \(a\gt0\) and \(a\ne1\).

\(\cos\theta=\dfrac{a^2+b^2}{2ab}\), where \(a,b\) are distinct and \(ab\gt0\).

The angle of elevation of the top of a tower is \(30^\circ\). If the height of the tower is doubled (observer fixed), then the angle of elevation also doubles.

If both the height of a tower and the distance of the point of observation from its foot increase by 10%, then the angle of elevation of its top remains unchanged.