Cot 565°- tan 205°/ tan 245° - cot 295° = a cos² 25° + b, then find the value of a+b
Answers
Given : (Cot 565°- tan 205°)/ (tan 245° - cot 295°) = a cos² 25° + b
To find : Value of a & b
Solution:
(Cot 565°- tan 205°)/ (tan 245° - cot 295°) = a cos² 25° + b
LHS
= (Cot 565°- tan 205°)/ (tan 245° - cot 295°)
565° = 360° + 205°
= (Cot 205°- tan 205°)/ (tan 245° - cot 295°)
= (Cot (180 + 25°) - tan(180 + 25°)/ (tan (180 + 65°) - cot(360 - 65°))
= (Cot 25° - tan 25°) / (tan 65° - (-cot(65°) )
= (Cot 25° - tan 25°) / (tan 65° + Cot65° )
=(Cot 25° - tan 25°) /(Cot25° + tan25° )
= (Cos25°/sin25° - Sin25°/Cos25°) / (Cos25°/sin25° + Sin25°/Cos25°) )
= (Cos ²25° - Sin ²25°) /( Cos ²25° + Sin ²25°)
= Cos ²25° - Sin ²25°
RHS = a cos² 25° + b
a = 1 , b = - Sin ²25°
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