त्रिकोणमिति का परिचय

Question

निम्नलिखित सर्वसमिकाएँ सिद्ध कीजिए, जहाँ वे कोण, जिनके लिए व्यंजक परिभाषित हैं, न्यून कोण है:
$fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction equals space 2 space secA$

Solution

L.H.S. = $fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction$
$equals space fraction numerator cos squared straight A plus left parenthesis 1 plus sinA right parenthesis squared over denominator left parenthesis 1 plus sinA right parenthesis space cos space straight A end fraction equals space fraction numerator cos squared straight A plus 1 plus sin squared straight A plus 2 space sinA over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator left parenthesis cos squared straight A plus sin squared straight A right parenthesis space plus space 2 space sinA space plus space 1 over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator 1 plus 2 space sinA space plus space 1 over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction space equals space fraction numerator 2 plus 2 space sinA over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator 2 space left parenthesis 1 plus sin space straight A right parenthesis over denominator left parenthesis 1 plus sin space straight A right parenthesis space cos space straight A end fraction equals 2 over cosA equals space 2 space sec space straight A space equals space straight R. straight H. straight S.$
अत: L.H.S. = R.H.S.

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