For any `triangleABC`, the value of determinant `|[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,cotC,1]|` is:

For any "Delta"A B C the value of determinant |sin^2\ \ A cot A1sin^2B cot B1sin^2\ \ C cot C1| is equal to- s in A s in B s in C b. 1 c. 0 d. s in A+s in B+s in C

If A+B+C=pi , then the value of the determinant D=|sin^2AcotA1sin^2BcotB1sin^2CcotC1|i se q u a lto 1 (b) -1 (c) 0 (d) None of these

In a Delta ABC , a, b, c are sides and A, B, C are angles opposite to them, then the value of the determinant |(a^(2),b sin A,c sin A),(b sin A,1,cos A),(c sin A,cos A,1)| , is

If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then (a) t a n A+t a n B+c (b) cotAcotBcotC (c) sin^2A+sin^2B+sin^2C (d) 0

If A, B, C are the angles of a triangle, then the determinant Delta = |(sin 2 A,sin C,sin B),(sin C,sin 2B,sin A),(sin B,sin A,sin 2 C)| is equal to

If the maximum and minimum values of the determinant |(1 + sin^(2)x,cos^(2) x,sin 2x),(sin^(2) x,1 + cos^(2) x,sin 2x),(sin^(2) x,cos^(2) x,1 + sin 2x)| are alpha and beta , then

If tanA=1 ,then find the value of sin^(2)A+cos^(2)A+cotA .

In a triangleABC, a^(2) sin 2C+c^(2) sin 2A=

Each question has four choices a, b, c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1. Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE. Statement 1: if A ,B ,C are the angles of a triangles and |[1, 1, 1], [ 1+sin A ,1+sinB, 1+sin C], [ sin A+sin^2A, sin B+sin^2B,sin C+sin^2C]|=0 , then triangle may not be equilateral Statement 2: if any two rows of a determinant are the same, then the value of that determinant is zero.

In any triangle ABC, show that : 2a sin (B/2) sin (C/2)=(b+c-a) sin (A/2)