If A=sin70o+sin20ocos70o+cos20o B=sin75o+sin15ocos75o+cos15o C=sin80o+sin10ocos80o+cos10o Then

A=sinα+sinβcosα+cosβ=2sin(α+β2)cos(α−β2)2cos(α+β2)cos(θ−β2)=tan45o=1 A=B=C=tan45o

If A=sin70o+sin20ocos70o+cos20o B=sin75o+sin15ocos75o+cos15o C=sin80o+sin10ocos80o+cos10o Then

A=sinα+sinβcosα+cosβ=2sin(α+β2)cos(α−β2)2cos(α+β2)cos(θ−β2)=tan45o=1 A=B=C=tan45o

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If $A = \frac{\sin 70^{o} + \sin 20^{o}}{\cos 70^{o} + \cos 20^{o}}$ $B = \frac{\sin 75^{o} + \sin 15^{o}}{\cos 75^{o} + \cos 15^{o}}$ $C = \frac{\sin 80^{o} + \sin 10^{o}}{\cos 80^{o} + \cos 10^{o}}$ Then

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$A = B = C$

$A < C < B$

$A > B > C$

$A < B < C$

answer is C.

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Detailed Solution

$A = \frac{\sin α + \sin β}{\cos α + \cos β} = \frac{2 \sin (\frac{α + β}{2}) \cos (\frac{α - β}{2})}{2 \cos (\frac{α + β}{2}) \cos (\frac{θ - β}{2})} = \tan 45^{o} = 1 A = B = C = \tan 45^{o}$

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If A=sin70o+sin20ocos70o+cos20o B=sin75o+sin15ocos75o+cos15o C=sin80o+sin10ocos80o+cos10o Then

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If $A = \frac{\sin 70^{o} + \sin 20^{o}}{\cos 70^{o} + \cos 20^{o}}$ $B = \frac{\sin 75^{o} + \sin 15^{o}}{\cos 75^{o} + \cos 15^{o}}$ $C = \frac{\sin 80^{o} + \sin 10^{o}}{\cos 80^{o} + \cos 10^{o}}$ Then