(sin α + cos α) (tan α + cot α) = sec α + cosec α. Prove the following statement

Solution:

LHS = (sin α + cos α) (tan α + cot α)

We know that tan α = sin α/cos α and cot α = cos α/sin α

= (sin α + cos α) (sin α/cos α + cos α/sin α)

By taking LCM

= (sin α + cos α) [(sin² α + cos² α)/cos α sin α]

As sin² α + cos² α = 1

= (sin α + cos α)/cos α sin α

It can be written as

= 1/cos α + 1/sin α

Here 1/cos α = sec α and 1/ sin α = cosec α

= sec α + cosec α

= RHS

Therefore, it is proved.

✦ Try This: Prove the following

(sin α + cosec α)² + (cosec α + sec α)² = tan² α + cot² α + 7.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 4

(sin α + cos α) (tan α + cot α) = sec α + cosec α. Prove the following statement

Summary:

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent,, secant, cosecant, and cotangent. It is proved that (sin α + cos α) (tan α + cot α) = sec α + cosec α

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