Question

cos^2 20°+cos^2 70°÷sin^2 59°+sin^2 31°

Answer 1

$\textbf{Given:}$

$\dfrac{cos^220^{\circ}+cos^270^{\circ}}{sin^259^{\circ}+sin^231^{\circ}}$

$\textbf{To find:}$

$\text{The value of \dfrac{cos^220^{\circ}+cos^270^{\circ}}{sin^259^{\circ}+sin^231^{\circ}} }$

$\textbf{Solution:}$

$\text{Using the following results,}$

$\boxed{\bf\,cos\theta=sin(90^{\circ}-\theta)}$

$\boxed{\bf\,sin\theta=cos(90^{\circ}-\theta)}$

$\implies\,cos\,70^{\circ}=sin\,20^{\circ}$

$sin\,31^{\circ}=cos\,59^{\circ}$

$\text{Consider,}$

$\dfrac{cos^220^{\circ}+cos^270^{\circ}}{sin^259^{\circ}+sin^231^{\circ}}$

$=\dfrac{cos^220^{\circ}+sin^220^{\circ}}{sin^259^{\circ}+cos^259^{\circ}}$

$\text{Using,}\;\boxed{\bf\,cos^2A+sin^2A=1}$

$=\dfrac{1}{1}$

$=1$

$\therefore\bf\,\dfrac{cos^220^{\circ}+cos^270^{\circ}}{sin^259^{\circ}+sin^231^{\circ}}=1$

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Answer 2

Answer:

we know that Sin^2 A + Cos^2 A = 1

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