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lana66690 [7]
3 years ago
5

Verify the identity by transforming the left-hand side into the right-hand side.

Mathematics
1 answer:
qaws [65]3 years ago
8 0
<span>(1 + cos² 3θ) / (sin² 3θ) = 2 csc² 3θ - 1

Starting with the left:  Note that  cos²θ + </span><span>sin²θ = 1.
In the same way:    </span><span>cos²3θ + <span>sin²3θ = 1
</span></span>Therefore                cos²3θ  = 1 - <span>sin²3θ
</span> From the top:  (1 + cos² 3θ) = 1 + 1 - sin²3θ = 2 - <span>sin²3θ
</span>
(1 + cos² 3θ) / (sin² 3θ) = (<span>2 - sin²3θ) / (sin² 3θ) = 2/</span><span>sin² 3θ - </span><span>sin²3θ/</span>sin²3θ

=  2/<span>sin² 3θ - 1;        But 1/</span><span>sinθ = csc</span><span>θ,  Similarly  </span>1/sin3θ = csc3θ

= 2 *(1/sin<span>3θ)²  - 1</span>
= 2csc²3θ  - 1.        Therefore  LHS = RHS.  QED.

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