Question

sin theta+cos theta=m then sin theta-cos theta=​

Answer 1

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➠ If sinθ + cosθ = m , then find the value sinθ - cosθ = ?

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❏ Trigonometry is one of the most important topic in modern mathematics that is useful in various field.

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❏ Here are simple formulas used frequently :

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; :\longmapsto sin^2\theta + cos^2\theta = 1$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; :\longmapsto (a+b)^2 = a^2 + b^2 + 2ab$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; :\longmapsto (a-b)^2 = a^2 + b^2 - 2ab$

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$\underline{\boxed{\bold{ \bigstar \; Given \; \bigstar }}}$  

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❏ sinθ + cosθ = m

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Let's Start !

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❖ Here is your answer :)

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$:\implies sin\theta + cos\theta = m$

$:\implies (sin\theta + cos\theta)^2 = m^2$

$:\implies sin^2\theta + cos^2\theta + 2sin\theta cos\theta = m^2$

$:\implies 1 + 2sin\theta cos\theta = m^2$

$:\implies 2sin\theta cos\theta = m^2 - 1$

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$\boxed{\bold{\orange{ :\leadsto \; 2sin\theta cos\theta = m^2 - 1}}}$

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☯ Now let's find value of (sinθ - cosθ) :

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$:\implies (sin\theta - cos\theta)^2 = sin^2\theta + cos^2\theta- 2sin\theta cos\theta$

$:\implies (sin\theta - cos\theta)^2 = 1- 2sin\theta cos\theta$

$:\implies (sin\theta - cos\theta)^2 = 1- (m^2-1)$

$:\implies (sin\theta - cos\theta)^2 = 1- m^2+1$

$:\implies (sin\theta - cos\theta)^2 = 2- m^2$

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$\boxed{\bold{\red{ :\leadsto sin\theta - cos\theta = \sqrt{(2- m^2)} }}}$

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$\boxed{\boxed{\bold{\therefore sin\theta - cos\theta = \sqrt{(2- m^2)} }}}$

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Hope this helps u.../

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