यदि frac{cos alpha}{sin beta} = n और frac{cos | vedclass

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(C) दिया गया है:$n = \frac{\cos \alpha}{\sin \beta} \implies \cos \alpha = n \sin \beta \quad (1)$$m = \frac{\cos \alpha}{\cos \beta} \implies \cos \a

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$\frac{n^2}{m^2 + n^2}$

Vedclass · Answer

(C) दिया गया है:$n = \frac{\cos \alpha}{\sin \beta} \implies \cos \alpha = n \sin \beta \quad (1)$$m = \frac{\cos \alpha}{\cos \beta} \implies \cos \alpha = m \cos \beta \quad (2)$$(1)$ और $(2)$ की तुलना करने पर:$n \sin \beta = m \cos \beta$दोनों पक्षों का वर्ग करने पर:$n^2 \sin^2 \beta = m^2 \cos^2 \beta$सर्वसमिका $\sin^2 \beta = 1 - \cos^2 \beta$ का उपयोग करने पर:$n^2 (1 - \cos^2 \beta) = m^2 \cos^2 \beta$$n^2 - n^2 \cos^2 \beta = m^2 \cos^2 \beta$$n^2 = (m^2 + n^2) \cos^2 \beta$अतः,$\cos^2 \beta = \frac{n^2}{m^2 + n^2}$.

यदि $\frac{\cos \alpha}{\sin \beta} = n$ और $\frac{\cos \alpha}{\cos \beta} = m$ है,तो $\cos^2 \beta$ का मान ज्ञात कीजिए।

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