समीकरण ` 4 cos theta + 5 sin theta = 5` को हल कीजिए , यदि `tan 51^(@) 21' = 5/4`

Explanation

माना `phi = 51^(@) 21'`
` :. tan phi = 5/4 `
` rArr sin phi = 5/(sqrt(41)) " और " cos phi = 4/(sqrt(41))`
अब ` 4 cos theta + 5 sin theta = 5 `
दोनों पक्षों को ` sqrt(4^(2) +5^(2))= sqrt(41)` से भाग देने पर
` 4/(sqrt(41)) cos theta + 5/(sqrt(41)) sin theta = 5/(sqrt(41))`
` rArr cos phi cos theta + sin phi sin theta = sin phi `
` rArr cos ( theta - phi) = cos (pi/2-phi)`
` rArr ( theta - phi) = 2npi pm (pi/2- phi)`
` rArr theta = 2npi + pi/2 `
ऋण चिन्ह लेने पर
` ( theta - phi) = 2npi - (pi/2-phi) `
` rArr theta = 2npi - pi/2 + 2 phi `
` rArr theta = 2npi - 90^(@) + 2 xx 51^(@) 21'`
` = 2n pi - 90^(@) + 102^(@) 42'`
` = 2npi + 12^(@) 42 ' `