Question

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 1

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

$\Rightarrow$2B + B = 180$°$
$\Rightarrow$3B = 180$°$
$\Rightarrow$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

$\Rightarrow$2 Sin 90$°$ - 3 Cos 90$°$ + 5 Cot 90$°$

$\Rightarrow$2 ( 1 ) - 3 ( 0 ) + 5 ( 0 ) ( As we know Sin 90$°$ = 1 , Cos 90$°$ = 0 and Cot 90$°$ = 0 )

$\Rightarrow$2 - 0 + 0

$\Rightarrow$2 ( Ans )