If the angles A,B,C of triangle ABC are in arithmetic progression with common difference 30.then,find the value of 2 sinC-3cosC+5cotC
Answer :
Given
Angles A , B , C are in A.P. and common difference = 30
SO,
We know
B - A = 30 ------------------( 1 )
C - B = 30 ------------------( 2 )
B - A = C - B
2B = A + C ----------------- ( 3 )
And we know in triangle
A + B + C = 180
substitute value from equation 3 and get
2B + B = 180
3B = 180
B = 60 ( Now substitute value of B in equation 2 and get )
C - 60 = 30
C = 90
So,
Value of
2 Sin C - 3 Cos C + 5 Cot C we substitute C = 90 , and get
2 Sin 90 - 3 Cos 90 + 5 Cot 90
2 ( 1 ) - 3 ( 0 ) + 5 ( 0 ) ( As we know Sin 90 = 1 , Cos 90 = 0 and Cot 90 = 0 )
2 - 0 + 0
2 ( Ans )