If asin- -bcos-m and acos- -bsin-n- prove that m2 - n2 - a2 - b2

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Vector Addition

If asinθ +b...

Question

If $a s i n θ + b c o s θ = m$ and $a c o s θ - b s i n θ = n$ , prove that $m^{2} + n^{2} = a^{2} + b^{2}$

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If $a cos θ - b sin θ = c$ , prove that $a sin θ + b cos θ = \pm \sqrt{a^{2} + b^{2} - c^{2}}$

a cos θ + b sin θ = m

a sin θ - b cos θ = n

a^{2} + b^{2} =

a cos θ + b sin θ = m

a sin θ - b cos θ = n

a^{2} + b^{2}

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