If θ be positive acute angle and 5cosθ + 12sinθ = 13, then the value of cosθ is
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5cosx + 12sinx = 13,
5 + 12tanx = 13secx,
Squarin both-sides,
25 +144tanx^2 +120tanx = 169sec^2x=169(tan^2x +1),
25(tanx)^2 - 120tanx + 144 = 0,
(5tanx - 12)^2 = 0,
tanx = 12/5. FROM THIS cosx is 5/13
5 + 12tanx = 13secx,
Squarin both-sides,
25 +144tanx^2 +120tanx = 169sec^2x=169(tan^2x +1),
25(tanx)^2 - 120tanx + 144 = 0,
(5tanx - 12)^2 = 0,
tanx = 12/5. FROM THIS cosx is 5/13
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