Question

Show that the following statement is an identity by transforming the left side into the right side. sin θ (sec θ + csc θ) = tan θ + 1 We begin by writing the left side in terms of sin θ and cos θ. We can then perform the multiplication and simplify in terms of tan θ. sin θ (sec θ + csc θ) = sin θ 1 + 1 sin θ = sin θ + sin θ sin θ = tan θ +_

Answer 1

Answer:

Step-by-step explanation:

Required to prove that:

Sin θ(Sec θ + Cosec θ)= tan θ+1

Steps:

Recall sec θ= 1/cos θ and cosec θ=1/sin θ

Substitution into the Left Hand Side gives:

Sin θ(Sec θ + Cosec θ)

= Sin θ(1/cos θ  + 1/sinθ )

Expanding the Brackets

=sinθ/cos θ + sinθ/sinθ

=tanθ+1 which is the Right Hand Side as required.

Note that from trigonometry sinθ/cosθ = tan θ