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यदि A = 45° तो sinA + cosA + tanA का मान है

(A) √2

(B) √2 + 1

(C) \(\frac{\sqrt 2 + 1}{\sqrt 2}\)

(D) 2 + √2

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सही विकल्प है (B) √2 + 1

दिया है

\(A=45^{\circ}\)

तो,

\( \sin A+\cos A+\tan A \)

\(=  \sin 45^{\circ}+\cos 45^{\circ}+\tan 45^{\circ}\)

\(=  \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}+\frac{1}{1}\)

\(=  \frac{1+1+\sqrt{2}}{\sqrt{2}}\)

\(=\frac{2+\sqrt{2}}{\sqrt{2}}\)

\(=\frac{2+\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\)

\( =\frac{2 \sqrt{2}+2}{2}\)

\( =\frac{\not2(\sqrt{2}+1)}{\not2}\)

\( =\sqrt{2}+1\)

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