If coshx=143, sinhx=cosθ and -π<θ<-π2, then sinθ=

TS EAMCET · Maths · Trigonometric Equations

If $\cos h x = \frac{\sqrt{14}}{3}, \sin h x = \cos θ$ and $- π < θ < - \frac{π}{2}$ , then $\sin θ =$

A $\frac{1}{3}$
B $\frac{2}{3}$
C $- \frac{1}{3}$
D $- \frac{2}{3}$

Verified Solution

Answer & Solution

Correct Answer

(D) $- \frac{2}{3}$

Step-by-step Solution

Detailed explanation

Given that coshx=143 sinh2x=cosh2x-1 =149-1 =59 sinhx=53=cosθ ∴ cosθ=53 sin2θ=1-cos2θ =1-59=49 ∴ sinθ=±23 Given that θ lies in III quadrant. ∴ sinθ=-23

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the items given in List-

I

with those of the items of List-

II

	List - $I$		List - $II$
$(a)$	If $y = \|x\| + \|x - 2\|$ then at $x = 2, \frac{d y}{d x} =$	$(i)$	$1$
$(b)$	If $f (x) = \|\cos 2 x\|$ , then $f^{'} (\frac{π}{4} +) =$	$(ii)$	$0$
$(c)$	If $f (x) = \sin π [x]$ where $[\cdot]$ denotes the greatest integer function, then $f^{'} (1 -) =$	$(iii)$	$- 2$
$(d)$	If $f (x) = \log \|x - 1\|, x \neq 1$ then $f^{'} (\frac{1}{2}) =$	$(iv)$	does not exits
		$(v)$	$\frac{1}{2}$

TS EAMCET 2018 Hard

Explore more questions on app

From TS EAMCET

Explore more questions on app