Prove the following identity : (1+ ^2 A ) A e c^2 A = A - Vidyadip

Question

Prove the following identity : $\frac{\left(1+\tan ^2 A\right) \cot A}{\cos e c^2 A}=\tan A$

✓

Answer

$\frac{\left(1+\tan ^2 A\right) \cot A}{\cos e c^2 A}$
$=\frac{\sec ^2 A \cot A}{\operatorname{cosec} 2} \ldots \ldots\left(\therefore \sec ^2 A=1+\tan ^2 A\right)$
$=\frac{\frac{1}{\cos ^2 A} \cdot \frac{\cos A}{\sin A}}{\frac{1}{\sin ^2 A}}=\frac{1}{\frac{\cos A \sin A}{\frac{1}{\sin ^2 A}}}$
$=\frac{\sin A}{\cos A}=\tan A$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[2 Mark Question Answer]" from Trigonometry→Trigonometry — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin:
will not be a Rs 2 coin?

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is: a black ace

Find the 20th term of the A.P. whose 7th term is 24 less than the 11th term, first term being 12.

Given $A=\left[\begin{array}{cc}2 & -6 \\ 2 & 0\end{array}\right], B=\left[\begin{array}{cc}-3 & 2 \\ 4 & 0\end{array}\right], C=\left[\begin{array}{ll}4 & 0 \\ 0 & 2\end{array}\right]$ Find the matrix $X$ such that $A+2 X=2 B+C$.

Prove.
$\tan^2A - \sin^2A = \tan^2A \sin^2A$

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting: a diamond

The equation of a line AB is 2x – 2y + 3 = 0
(i) Find the slope of line AB.
(ii) Calculate the angle that the line AB makes with the positive direction of the x-axis.

A bag contains $100$ identical marble stones which are numbered $1$ to $100.$ If one stone is drawn at random from the bag, find the probability that it bears: a number divisible by $4$ or $5$

A coin is tossed once. Find the probability of : not getting a tail

If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.