Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(B)

Question 1

Prove that:

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii) 

(viii) 

(ix) 

Solution 1

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Question 2

If = m and = n, then prove that x² + y² = m² + n².

Solution 2

Question 3

If m= and n= , prove that 

Solution 3

Question 4

If , prove that 

Solution 4

Question 5

If and , prove that 

Solution 5

Given:

and

Question 6

If , prove that 

Solution 6

Question 7

If  and , show that (m² + n²) cos²B = n².

Solution 7

LHS = (m² + n²) cos²B

Hence, (m² + n²) cos²B = n².