Question

if sin 5A = cos4A find sin3A+cos6A+tan3A​

Answer 1

❏ Used ForMuLaS:-

➾ X+Y=90°, then

$\sf\longrightarrow \sin X=\cos(90\degree-X)$

$\sf\longrightarrow \sec X=\cosec(90\degree-X)$

$\sf\longrightarrow \tan X=\cot(90\degree-X)$

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❏ Question:-

Q) Find the value of ,

$\sf\longrightarrow\sin3 A + \cos6A+tan3A=?$

where, $\sf\longrightarrow \sin5A=\cos4A$

❏ Solution:-

❚➾

$\sf\longrightarrow \sin5A=\cos4A$

$\sf\longrightarrow \sin5A=\sin(90\degree-4A)$

$\sf\longrightarrow 5A=(90\degree-4A)$

$\sf\longrightarrow 5A+4A=90\degree$

$\sf\longrightarrow 9A=90\degree$

$\sf\longrightarrow A=\frac{\cancel{90}\degree}{\cancel{9}}$

$\sf\longrightarrow\boxed{ \large{\red{A=10\degree}}}$

$\sf\therefore\sin3 A +\cos6A+tan3A$

$\sf\longrightarrow \sin3 (10\degree)+\cos6(10\degree)+tan3(10\degree)$

$\sf\longrightarrow \sin30\degree+\cos60\degree+\tan30\degree$

$\sf\longrightarrow \frac{1}{2}+\frac{1}{2}+\frac{1}{\sqrt{3}}$

$\sf\longrightarrow 1+\frac{1}{\sqrt{3}}$

$\sf\longrightarrow \frac{\sqrt{3}+1}{\sqrt{3}}$

[ rationalising the denominator ]

$\sf\longrightarrow \frac{(\sqrt{3}+1)\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}$

$\sf\longrightarrow\boxed{\large{\red{ \frac{3+\sqrt{3}}{3}}}}$

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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