Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

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Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

If $sin θ - cos θ = \sqrt{2} sin θ$ $sintheta-costheta=sqrt(2)sintheta$ , then prove that, $sin θ + cos θ = - \sqrt{2} cos θ$ $sintheta+costheta=-sqrt(2)costheta$

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Answer 1 · 2018-03-17T12:42:05

$sin θ + cos θ = - \sqrt{2} cos θ$ $sintheta+costheta=-sqrt(2)costheta$

Explanation:

Here,
$sin θ - cos θ = \sqrt{2} sin θ$ $sintheta-costheta=sqrt(2)sintheta$
$\Rightarrow sin θ - \sqrt{2} sin θ = cos θ$ $=>sintheta-sqrt(2)sintheta=costheta$
$\Rightarrow sin θ (1 - \sqrt{2}) = cos θ$ $=>sintheta(1-sqrt(2))=costheta$
$\Rightarrow sin θ [(1 - \sqrt{2}) (\frac{1 + \sqrt{2}}{1 + \sqrt{2}})] = cos θ$ $=>sintheta[(1-sqrt(2))((1+sqrt(2))/(1+sqrt(2)))]=costheta$
$\Rightarrow sin θ [\frac{1 - 2}{1 + \sqrt{2}}) = cos θ$ $=>sintheta[(1-2)/(1+sqrt(2)))=costheta$
$\Rightarrow sin θ (- 1) = (1 + \sqrt{2}) cos θ$ $=>sintheta(-1)=(1+sqrt(2))costheta$
$\Rightarrow - sin θ = cos θ + \sqrt{2} cos θ$ $=>-sintheta=costheta+sqrt(2)costheta$
$\Rightarrow - sin θ - cos θ = \sqrt{2} cos θ$ $=>-sintheta-costheta=sqrt(2)costheta$
$\Rightarrow sin θ + cos θ = - \sqrt{2} cos θ$ $=>sintheta+costheta=-sqrt(2)costheta$

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Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

If $sin θ - cos θ = \sqrt{2} sin θ$ $sintheta-costheta=sqrt(2)sintheta$ , then prove that, $sin θ + cos θ = - \sqrt{2} cos θ$ $sintheta+costheta=-sqrt(2)costheta$

1 Answer

Explanation:

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Science

Math

Humanities

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Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

If sinθ−cosθ=√2sinθsintheta-costheta=sqrt(2)sintheta, then prove that, sinθ+cosθ=−√2cosθsintheta+costheta=-sqrt(2)costheta

1 Answer

Explanation:

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Impact of this question

If $sin θ - cos θ = \sqrt{2} sin θ$ $sintheta-costheta=sqrt(2)sintheta$ , then prove that, $sin θ + cos θ = - \sqrt{2} cos θ$ $sintheta+costheta=-sqrt(2)costheta$