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Question: If \(\cos(180^{o} + 80^{o}) = \cos(180^{o} - 80^{o})\), then \(\cos 260{^\circ}\)=...

If cos⁡(180o+80o)=cos⁡(180o−80o)\cos(180^{o} + 80^{o}) = \cos(180^{o} - 80^{o}), then cos⁡260∘\cos 260{^\circ}=

A

cos⁡260∘andcos⁡100∘\cos 260{^\circ}\text{and}\cos 100{^\circ}

B

θ=100∘\theta = 100{^\circ}

C

≥\geq

D

12(2sin⁡x+2cos⁡x)≥2sin⁡x.2cos⁡x\frac{1}{2}(2^{\sin x} + 2^{\cos x}) \geq \sqrt{2^{\sin x}.2^{\cos x}}

Answer

θ=100∘\theta = 100{^\circ}

Explanation

Solution

=s(s−c)ab{(s−as−b) ab+(s−bs−a) ab}= \sqrt{\frac{s(s - c)}{ab}}\left\{ \sqrt{\left( \frac{s - a}{s - b} \right)\ ab} + \sqrt{\left( \frac{s - b}{s - a} \right)\ ab} \right\}

s(s−c){s−a+s−b(s−a)(s−b)}=s(s−c){2s−a−b(s−a)(s−b)}=cs(s−c)(s−a)(s−b)=ccot⁡C2\sqrt{s(s - c)}\left\{ \frac{s - a + s - b}{\sqrt{(s - a)(s - b)}} \right\} = \sqrt{s(s - c)}\left\{ \frac{2s - a - b}{\sqrt{(s - a)(s - b)}} \right\} = c\sqrt{\frac{s(s - c)}{(s - a)(s - b)}} = c\cot\frac{C}{2} a=1,a = 1, b=3,b = \sqrt{3}, = 45o.