Question

Evaluate
$\bf \dfrac{\sin^{2} 63^{\circ} + \sin^{2}27^{\circ}}{\cos^{2}17^{\circ}+ \cos^{2} 73^{\circ}}$

Answer 1

$\large\pmb{\sf{Question :}}$

Evaluate: $\bf \dfrac{\sin^{2} 63^{\circ} + \sin^{2}27^{\circ}}{\cos^{2}17^{\circ}+ \cos^{2} 73^{\circ}}$

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$\large\pmb{\sf{Solution :}}$

$\sf{: \mapsto \dfrac{\sin^{2} 63^{\circ} + \sin^{2}27^{\circ}}{\cos^{2}17^{\circ}+ \cos^{2} 73^{\circ}}}$

$\sf{: \mapsto \dfrac{\sin^{2} (90 - 27)^{\circ} + \sin^{2}27^{\circ}}{\cos^{2}(90 - 73)^{\circ}+ \cos^{2} 73^{\circ}}}$

$\sf{: \mapsto \dfrac{\cos^{2} 27^{\circ} + \sin^{2}27^{\circ}}{\sin^{2}73^{\circ}+ \cos^{2} 73^{\circ}}}$

$\footnotesize\color{maroon}{\boxed{ \sf{\cos(90 - \theta) = \sin \theta \: \: \: \& \: \: \:\sin(90 - \theta) = \cos \theta}}}$

$\sf{ : \mapsto \frac{1}{1} }$

$\footnotesize\color{maroon}{\boxed{\sf{\because \sin^2 A + \cos^2 A = 1}}}$

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$\large\pmb{\sf{Final \: Answer :}}$

$\color{green}\underline{\underline{{ \boxed{ \sf{\dfrac{\sin^{2} 63^{\circ} + \sin^{2}27^{\circ}}{\cos^{2}17^{\circ}+ \cos^{2} 73^{\circ}} = 1}}}}}$

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$\large\pmb{\sf{Note :}}$

If an expression contains a trigonometric function firstly convert the trigonometric function into trigonometric identities. The relation of trigonometric identities in the expression is used to evaluate the value of the given expression.Students should remember the trigonometric identities and standard angles for solving these types of questions.

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$\large\pmb{\sf{Hint :}}$

The expression containing trigonometric functions can be evaluated from the relation of trigonometric identities. This expression is related to trigonometric ratios of complementary angles, two angles are said to be complementary if their sums equals 90 degrees. Applying the trigonometric identity we get the required answer.

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$\large\pmb{\sf{Learn \: More :}}$

Complete trigonometry table $\green \downarrow$

• brainly.in/question/32347977

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Answer 2

$\huge\bold{Note\: that}$

$\sf\color{red}sin\:x\:=\:cos\:(90−x)\:$

$\sf\color{pink}=\:sin²\:(63)\:+\:sin²\:(27)/\:cos²\:(17)+\:cos²(73)\:$

$\sf\color{green}=sin²\:(63)+cos²\:(90−27)/cos²(17)\:+sin²\:(90−73)$

$\sf\color{blue}=sin²(63)\:+cos²\:(63)/cos²(17)\:+\:sin²(17)$

And using the fact that sin²x+cos²x=1:

$1 \div 1$

$\sf\color{gold}=1$

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