Simplifying Trigonometric Expressions 8

Reorder the steps that simplify the following trig expression

$$\frac{\cot\left(90\degree-\theta\right)}{\cos\left(90\degree-\theta\right)}$$

TRIG EXPRESSION

$$\frac{\csc^2\theta-\cot^2\theta}{\cos^2\theta}$$

STRATEGY

Use 1 Pythagorean Identity

$$ID\ \rightarrow\ EXP$$

Apply the above strategy

Submit $$EXP$$

TRIG EXPRESSION

$$\frac{\csc^2\theta-\cot^2\theta}{\cos^2\theta}$$

SIMPLIFIED TRIG EXPRESSION

Submit $$EXP$$

TRIG EXPRESSION

$$\frac{\sin^2\theta+\sin^2\theta\ \tan^2\theta}{\sec^2\theta}$$

STRATEGY

(Algebra) Undistribute

$$ALG\ \rightarrow\ EXP$$

Apply the above strategy

Submit $$EXP$$

NOTE: Multiplication is implied

TRIG EXPRESSION

$$\frac{\sin^2\theta+\sin^2\theta\ \tan^2\theta}{\sec^2\theta}$$

SIMPLIFIED EXPRESSION

Submit $$EXP$$

$$SIMPLIFY\ \rightarrow\ \sin\theta\ \csc\left(90\degree-\theta\right)$$

Step 1 $$ID\ \rightarrow\ \sin\theta\ \cdot$$ ​ (a)   Step 2 $$ID\ \rightarrow\ \sin\theta\ \cdot$$ ​ (b)  

Step 3 $$ALG\ \rightarrow\$$ ​ (c)   Step 4 $$ID\ \rightarrow\$$ ​ (d)  

TRIG EXPRESSION

$$\left(1+\tan^2\theta\right)\left(1-\cos^2\theta\right)$$

STRATEGY

Apply 2 Pythagorean Identities

$$ID\ \rightarrow\ EXP$$

Apply the above strategy

Submit $$EXP$$

NOTE: Multiplication is implied

TRIG EXPRESSION

$$\left(1+\tan^2\theta\right)\left(1-\cos^2\theta\right)$$

SIMPLIFIED TRIG EXPRESSION

Submit $$EXP$$

SIMPLIFYING TRIG EXPRESSIONS

Is the following trig equation valid?

$$\cos\theta-\cos\theta\ \sin^2\theta=\sin^2\theta$$