Solve the following if A and B are vectors- a-A2 - B2 - 2AB cos -

a.√(| A #160; | #160; ^ 2 +| B #160; | #160; ^ 2 +2| A #160; | | B #160; | cosθ #160; #160; ) a.√(| A + B #160; | #160 ...

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Trigonometric Ratios of Compound Angles

Solve the fol...

Question

Solve the following if A and B are vectors:
$a \sqrt{A^{2} + B^{2} + 2 A B c o s θ}$

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Solution

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(a^{2} - b^{2}) sin θ + 2 a b cos θ = a^{2} + b^{2}

tan θ = \frac{a^{2} - b^{2}}{2 a b}

(a^{2} - b^{2}) sin θ + 2 a b cos θ = a^{2} + b^{2}

tan θ

(a^{2} - b^{2}) sin θ + 2 a b cos θ = a^{2} + b^{2}

tan θ

\to R = (\to A + \to B),

R^{2} = A^{2} + B^{2} + 2 A B c o s θ

R = \sqrt{A^{2} + B^{2} + 2 A B c o s θ}

60^{0}

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