Consider the following statements:I. If P, Q and R are the angles of t

1.	Consider the following statements:I. If P, Q and R are the angles of triangle then tan (P + Q)/2 = sec (R/2)II. Sin (X + Y)/2 = Cos (Z/2) only possible if X + Y + Z = 180°Find which statement is/are correct?1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2
Answer» Correct Answer - Option 2 : Only 2 Given: Two statements are given Formula Used: Basic concept of trigonometric ratio and identities We know that if A, B and C is the angles of triangle or their sum is 180° ∴ tan (A + B)/2 = cot (C/2) ∴ sin (A + B)/2 = cos (C/2) ∴ sec (A + B)/2 = cosec (C/2) Where versa vice is possible Calculation: P, Q and R are the angles of a triangle ∴ tan (P + Q)/2 = cot (R/2) But it is given in statement I tan (P + Q)/2 = sec (R/2) ∴ Statement 1 is incorrect Now, X + Y + Z = 180° ∴ Sin (X + Y)/2 = Cos (Z/2) So, Statement 2 is correct Hence, option (2) is correct

Consider the following statements:I. If P, Q and R are the angles of triangle then tan (P + Q)/2 = sec (R/2)II. Sin (X + Y)/2 = Cos (Z/2) only possible if X + Y + Z = 180°Find which statement is/are correct?1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 2 : Only 2

Given:

Two statements are given

Formula Used:

Basic concept of trigonometric ratio and identities

We know that if A, B and C is the angles of triangle or their sum is 180°

∴ tan (A + B)/2 = cot (C/2)

∴ sin (A + B)/2 = cos (C/2)

∴ sec (A + B)/2 = cosec (C/2)

Where versa vice is possible

Calculation:

P, Q and R are the angles of a triangle

∴ tan (P + Q)/2 = cot (R/2)

But it is given in statement I

tan (P + Q)/2 = sec (R/2)

∴ Statement 1 is incorrect

Now, X + Y + Z = 180°

∴ Sin (X + Y)/2 = Cos (Z/2)

So, Statement 2 is correct

Hence, option (2) is correct