Question
If cos 39Ā° = x/ ā(x2 + y2),Ā
Ā then the value of tan 51Ā° = ?Solution
cos 39Ā° = x/ ā(x 2Ā + y 2) =Ā Ā Base/hypotenuse So base = x &Ā hypotenuse =Ā 
so perpendicular = y But for angle 51Ā° which is complimentary of 39Ā° , perpendicular =y & base = x. So tan 51Ā° = base/perpendicularĀ =Ā Alternate Method : cos 39Ā° =Ā ORĀ sin (90Ā°-39Ā°)Ā =Ā OR sin 51Ā° =Ā Ā Ā -----(1) Squaring on both sides, we will get, sin2 51Ā° =Ā or 1 - cos2 51Ā° =Ā or cos2 51Ā° = 1 -Ā =Ā So cos 51Ā° =Ā Ā ----(2) Hence tan 51Ā° = sin51Ā°/ cos51Ā° =
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