**Trigonometric Ratios Complementary Angles CBSE NCERT Solutions Chapter 8 Exercise 8.4 Question 5**

**5.** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

**(i)**

**Solution:**

**L.H.S =**

**R.H.S = **

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(ii) **

**L.H.S =**

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(iii) **

**L.H.S =**

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(iv) **

**L.H.S **=

**R.H.S =**

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(v)**

**Solution:**

**L.H.S=**

**R.H.S **

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(vi) **

**L.H.S **

**R.H.S **

Therefore,** L.H.S = R.H.S**

**Hence, Proved**

**(vii)**

**L.H.S =**

**Therefore, L.H.S = R.H.S**

**Hence Proved**

**(viii)**

**L.H.S **=

**Therefore, L.H.S = R.H.S**

**Hence Proved**

**(ix) **

**L.H.S**

**R.H.S **=

Therefore, **L.H.S = R.H.S**

**Hence Proved**

**(x) **

Therefore,

**Hence Proved**