Question
Prove.
$\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{\cos A}{1+\sin A}$
$\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{\cos A}{1+\sin A}$
✓
Answer
$\text { LHS }=\sqrt{\frac{1-\sin A}{1+\sin A}} $
$=\sqrt{\frac{1-\sin A}{1+\sin A} \times \frac{1+\sin A}{1+\sin A}}$
$ =\sqrt{\frac{1-\sin ^2 A}{(1+\sin A)^2}} $
$ =\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}} $
$\frac{\cos A}{1+\sin A}=\text { RHS }$
$=\sqrt{\frac{1-\sin A}{1+\sin A} \times \frac{1+\sin A}{1+\sin A}}$
$ =\sqrt{\frac{1-\sin ^2 A}{(1+\sin A)^2}} $
$ =\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}} $
$\frac{\cos A}{1+\sin A}=\text { RHS }$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the radius of the sphere whose surface area is equal to its volume .
The bisector of ∠ B and ∠C of a quadrilateral ABCD intersect in P, show that P is equidistant from the opposite sides AB and CD.
Part of a geometrical figure is given in each of the diagrams below. Complete the figures so. that the line AB in each case is a line of symmetry of the completed figure.
Give also the geometrical name for the completed figure. Recognizable free hand Sketches would be awarded full marks.
Give also the geometrical name for the completed figure. Recognizable free hand Sketches would be awarded full marks.
A die is thrown once. Find the probability of getting a number : less than 8
Complete the following figure, about the given lines of symmetry which are shown by dotted lines and name the figure thus obtained:
Mr. R.K. Nair gets Rs 6,455 at the end of one year at the rate of 14% per annum in a recurring deposit account. Find the monthly installment.
In the figure alongside, OAB is a quadrant of a circle. The radius $OA = 3.5 cm$ and $OD = 2 cm$. Calculate the area of the shaded $22$ portions.
→If $a: b:: c: d:: e: f$, then prove that $\frac{a e+b f}{a e-b f}=\frac{c e+d f}{c e-d f}$
→One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting: a black face card
Describe the locus for questions 1 to 13 given below:
The locus of the moving end of the minute hand of a clock.