1 Q-6 Prove that cos cosa+cosß (1+c...
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1 Q-6 Prove that cos cosa+cosß (1+cosacosß) = 2 tan-1

JEE/Engineering Exams
Maths
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Let ( & e g ) ( 0 quad cos x=frac{cos x+cos beta}{1+cos alpha cdot cos beta}=frac{left(1-tan ^{2} frac{alpha}{2} cdot tan ^{2} frac{beta}{2}right)}{left(1+tan ^{2} frac{alpha}{2}+tan ^{2} frac{beta}{2}right)} ) ( 00 cos ^{-1} x=tan ^{-1}left(frac{2 tan ^{2} alpha_{2} cdot tan beta / 2}{log tan ^{2} frac{alpha}{2} cdot tan ^{2} frac{beta}{2}}right) ) Now assume ( [tan alpha / 2 cdot tan beta mid 2]=y ) So, we know that ( 2 tan ^{-1} y=tan ^{-1}left(frac{2 y}{1-y^{2}}right) ) Similarly, we get: ( cos ^{-1}(x)=2 tan ^{-1}(y) ), ( 0^{circ} ) o ( cos ^{-1}left(frac{cos alpha+cos beta}{1+cos alpha cdot cos beta}right)=2 tan ^{-1}left(tan frac{alpha}{2} cdot tan frac{beta}{2}right) )
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