Prove- cos -14-5-cos -112-13-cos -133-65

Given,cos^ 14/5+cos^ 112/13=cos^ 133/65 Starting with LHS, LHS= cos^ 1 ( 4/5 )+cos^ 1 ( 12/13 ) =cos^ 1 ( 4/5.12/13 √(1 ( 4/5 )^2)√(1 ( 12/13 )^2) ) [∵ cos ...

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Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

Prove, cos -1...

Question

Prove, $c o s^{- 1} \frac{4}{5} + c o s^{- 1} \frac{12}{13} = c o s^{- 1} \frac{33}{65}$

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Solution

Given, $c o s^{- 1} \frac{4}{5} + c o s^{- 1} \frac{12}{13} = c o s^{- 1} \frac{33}{65}$

Starting with LHS,
$L H S = c o s^{- 1} (\frac{4}{5}) + c o s^{- 1} (\frac{12}{13}) = c o s^{- 1} (\frac{4}{5} . \frac{12}{13} - \sqrt{1 - {(\frac{4}{5})}^{2}} \sqrt{1 - {(\frac{12}{13})}^{2}}) [∵ c o s^{- 1} x + c o s^{- 1} y = c o s^{- 1} (x y - \sqrt{1 - x^{2}} \sqrt{1 - y^{2}})] = c o s^{- 1} (\frac{48}{65} - \sqrt{{(\frac{3}{2})}^{2}} \sqrt{{(\frac{5}{13})}^{2}}) = c o s^{- 1} (\frac{48}{65} - \frac{3}{5} \times \frac{5}{13}) = c o s^{- 1} (\frac{48}{65} - \frac{3}{13}) = c o s^{- 1} (\frac{33}{65}) = R H S$

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Similar questions

{sin}^{- 1} \frac{3}{5} + {cos}^{- 1} \frac{12}{13} = {cos}^{- 1} \frac{33}{65}

Q. Prove that:

{cos}^{- 1} \frac{4}{5} + {sin}^{- 1} \frac{5}{13} = {cos}^{- 1} \frac{33}{65}

Q. Prove that

{s i n}^{- 1} (\frac{3}{5}) + {c o s}^{- 1} (\frac{12}{13}) = {s i n}^{- 1} (\frac{56}{65})

Q. Prove that :

{s i n}^{- 1} \frac{3}{5} - {c o s}^{- 1} \frac{12}{13} = {s i n}^{- 1} \frac{16}{65}

Prove, $c o s^{- 1} \frac{12}{13} + s i n^{- 1} \frac{3}{5} = s i n^{- 1} \frac{56}{65}$

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Prove, cos−145+cos−11213=cos−13365

Given,cos−145+cos−11213=cos−13365 Starting with LHS, LHS=cos−1(45)+cos−1(1213)=cos−1(45.1213−√1−(45)2√1−(1213)2)[∵cos−1x+cos−1y=cos−1(xy−√1−x2√1−y2)]=cos−1(4865−√(32)2√(513)2)=cos−1(4865−35×513)=cos−1(4865−313)=cos−1(3365)=RHS

Prove, $c o s^{- 1} \frac{4}{5} + c o s^{- 1} \frac{12}{13} = c o s^{- 1} \frac{33}{65}$