Prove the following trigonometric identities. 1+ ^2A =1 1- - Vidyadip

Question

Prove the following trigonometric identities.
$\frac{1+\cos\text{A}}{\sin^2\text{A}}=\frac{1}{1-\cos\theta}$

✓

Answer

We know that $\sin^2\text{A}+\cos^2\text{A}=1$
$\sin^2\text{A}=1-\cos^2\text{A}$
$\Rightarrow\ \sin^2\text{A}=(1-\cos\text{A})(1+\cos\text{A})$
$\Rightarrow\ \text{L.H.S}=\frac{(1+\cos\text{A})}{(1-\cos\text{A})(1+\cos\text{A})}=\frac{1}{1-\cos\text{A}}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$
Hence proved.

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 Marks Questions" from Trigonometric Identities→Trigonometric Identities — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

If $\text{cosec }\theta-\cot\theta=\alpha,$ write the value of $\text{cosec }\theta+\cos\alpha$.

Determine the nature of the root of the following quadratic equation:
$\frac{3}{5}\text{x}^2-\frac{2}{3}\text{x}+1=0$

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{987}{10500}$

A die is thrown once. What is the probability of getting a number lying between 2 and 6?

Find the sum of the following APs:
2, 7, 12, 17, .... to 19 terms.

Determine the nature of roots of the following quadratic equation.
m² + 2m + 9 = 0

If A, B, C are the interior angles of a $\triangle\text{ABC},$ show that:
$\cos\frac{\text{B+C}}{2}=\sin\frac{\text{A}}{2}$

Solve the following quadratic equation by using formula method:
$4 x^2+x-5=0$

Prove The Theorem : The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corrosponding intercepts made on any other transversal by the same parallel lines.

Form the quadratic equation from the roots given below : $\frac{1}{2},-\frac{1}{2}$