Evaluate the following - cos2 13- - sin2 77-

It is known that cos(90^o θ)=sin θ We have, cos^2 13^∘ sin^2 77^∘ = cos^2(90^∘ 77^∘) sin^2 77^∘ = sin^2 77^∘ ...

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Standard X

Mathematics

Complementary Trigonometric Ratios

Evaluate the ...

Question

Evaluate the following :
$c o s^{2} 13^{\circ} - s i n^{2} 77^{\circ}$

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Solution

It is known that $c o s (90^{o} - θ) = s i n θ$

We have,
$c o s^{2} 13^{\circ} - s i n^{2} 77^{\circ} = c o s^{2} (90^{\circ} - 77^{\circ}) - s i n^{2} 77^{\circ} = s i n^{2} 77^{\circ} - s i n^{2} 77^{\circ} = 0$

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Evaluate the following :cos213∘−sin277∘

It is known that cos(90o−θ)=sin θWe have,cos2 13∘−sin277∘=cos2(90∘−77∘)−sin277∘=sin277∘−sin277∘=0

Evaluate the following :
$c o s^{2} 13^{\circ} - s i n^{2} 77^{\circ}$

It is known that $c o s (90^{o} - θ) = s i n θ$

We have,
$c o s^{2} 13^{\circ} - s i n^{2} 77^{\circ} = c o s^{2} (90^{\circ} - 77^{\circ}) - s i n^{2} 77^{\circ} = s i n^{2} 77^{\circ} - s i n^{2} 77^{\circ} = 0$