1. ## comprehension -/sinx-cosx/=√1-sin2x

comprehension -
/sinx-cosx/=√(1-sin2x)
here '/ /' are depicting mode

Q1. cos x>sinx then x belongs to
1) (0,pi/2)
2) (pi/2,pi)
3) (pi,5pi/4)
4) (5pi/4,9pi/4)

Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
(3/4)
(1/4)
(5/4)
(7/4)

2. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by gurparwaan
comprehension -
/sinx-cosx/=√(1-sin2x)
here '/ /' are depicting mode

Q1. cos x>sinx then x belongs to
1) (0,pi/2)
2) (pi/2,pi)
3) (pi,5pi/4)
4) (5pi/4,9pi/4)

Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
(3/4)
(1/4)
(5/4)
(7/4)
$\displaystyle \sqrt{1-\sin(2x)} =$

$\displaystyle \sqrt{1 - 2\sin{x}\cos{x}} =$

$\displaystyle \sqrt{\sin^2{x} - 2\sin{x}\cos{x} + \cos^2{x}} =$

$\displaystyle \sqrt{(\sin{x} - \cos{x})^2} =$

$\displaystyle |\sin{x} - \cos{x}|$

3. ## Re: comprehension -/sinx-cosx/=√1-sin2x

solve first question on the basis of comprehension

4. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by gurparwaan
solve first question on the basis of comprehension
what do you mean by "comprehension" ?

5. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by skeeter
what do you mean by "comprehension" ?
its a section which comes in competitive exams where u r given a littlle detail and on that basis u r given some questions

6. ## Re: comprehension -/sinx-cosx/=√1-sin2x

what I posted is a proof that ...

$\displaystyle |\sin{x}-\cos{x}| = \sqrt{1-\sin(2x)}$

... is that not sufficient? otherwise, I do not understand what it is you are looking for.

7. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Q.1
Write $\displaystyle \sin(x)=\cos \left(\frac{\pi}{2}-x\right)$ or $\displaystyle \cos(x)=\sin \left(\frac{\pi}{2}-x\right)$

8. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by gurparwaan
Q2. Cos^2(3pi/4) + Cos^2(4pi/5)
(3/4)
(1/4)
(5/4)
(7/4)
should this be ...

$\displaystyle \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)$

... a typo perhaps ?

9. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by skeeter
should this be ...

$\displaystyle \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)$

... a typo perhaps ?
yes.

10. ## Re: comprehension -/sinx-cosx/=√1-sin2x

Originally Posted by skeeter
$\displaystyle \cos^2\left(\frac{3\pi}{4}\right) + \cos^2\left(\frac{4\pi}{3}\right)$
recommend you derive and learn the trig values of the special angles on the unit circle ...