CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Trigonometric Identities. Our task is to simplify the given expression in terms of t. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 14: If \\frac {2Sinx}{1+cosx+Sinx}\\)=t, \\frac{1–Cosx+Sinx}{1+Sinx}\\) can be written as:

1. 1/t
2. t
3. √t Sec x
4. \\frac{t}{Sinx}\\)

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Simplify the expression to get the answer!

= \\frac{(2 Sin x) }{(1+cosâ?¡ x + Sinx)}\\) * \\frac{(1+Sinâ?¡ x - Cos x) }{(1+Sinâ?¡x - Cos x)}\\)
= 2 Sin x *\\frac{(1 + Sin x – Cos x)}{((1 + Sin x)^2 – Cos^2 x)}\\)
= 2 Sin x * \\frac{(1 + Sin x – Cos x)}{(1 + Sin^2 x + 2 Sin x – Cos^2 x)}\\)
= 2 Sin x * \\frac{(1 + Sin x – Cos x)}{(Cos^2 x + Sin^2 x + Sin^2 x + 2 Sin x – Cos^2 x)}\\)

(Since, 1 = Cos²x + Sin ²x)
= 2 Sin x * \\frac{(1 + Sin x – Cos x)}{(2 Sin^2 x + 2 Sin x)}\\)
= 2 Sin x * \\frac{(1 + Sin x – Cos x)}{(2 Sin x (1 + Sin x))}\\)
= \\frac{(1 – Cos x + Sin x)}{(1 + Sin x)}\\) = t

The question is "If \\frac{(2Sinx)}{(1+cosx+Sinx)}\\)=t, \\frac{(1–Cosx+Sinx)}{(1+Sinx)}\\) can be written as"

Hence, the answer is t

Choice B is the correct answer.