Question

please solve this MATHS question...

no wrong answers please ..
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Answer 1

SOLUTION:

Let us assume that sin^-1(3/5) = x and sin^-1(8/17) = y.

$\implies \bf \: \sin ^{ - 1} \bigg( \frac{3}{5} \bigg ) = x \\ \\ \implies \bf \: \sin \: x = \bigg( \frac{3}{5} \bigg ) \\ \\ \implies \bf \: \cos \: x \: = \sqrt{1 - \sin ^{2} x} \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{3}{5} \bigg) ^{2} } \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{9}{5} \bigg )} \\ \\ \implies \bf \: \frac{4}{5} \\ \\ \implies \bf \: \cos \: x \: = \frac{4}{5}$

now find the value of of sin y

$\implies \bf \sin ^{ - 1} \bigg( \frac{8}{17} \bigg) \: = y \\ \\ \implies \bf \sin \: y \: = \frac{8}{17} \\ \\ \implies \bf \sin \: y = \sqrt{1 - \sin^{2} y} \\ \\ \implies \: \bf \sqrt{1 - \bigg( \frac{8}{17} \bigg)^{2} } \\ \\ \implies \: \bf \: \sqrt{1 - \bigg( \frac{64}{289} \bigg) } \\ \\ \implies \: \bf \: \frac{15}{7} \\ \\ \implies \bf \: \sin \: y = \frac{15}{7}$

As we know that cos(a-b) = cos a cos b + sin a sin b.

$\implies \bf \: \cos(x - y) = \: \frac{4}{5} \times \frac{15}{7} + \frac{3}{5} \times \frac{8}{17} \\ \\ \implies \bf \: \cos(x - y) = \frac{60 + 24}{17 \times 5} \\ \\ \implies \bf \cos(x - y) = \frac{84}{85} \\ \\ \implies \bf \: (x - y) \ = cos ^{ - 1} \bigg(\frac{84}{85} \bigg)$

Putting the value of x and y we get,

$\implies \bf \sin ^{ - 1} \frac{3}{5} - \sin ^{ - 1} \frac{8}{7} = \cos ^{ - 1} \frac{84}{85}$

LHS = RHS

HENCE PROVED

Answer 2

YARR 50 points ke Question kyu Nahi puchte ???