Question

 

Which of the following is equivalent to the expression? 

	A.
	B.
	C.
	D.

Which of the following is equivalent to the expression? 

	A.
	B.
	C.
	D.

 

Answer 1

1)

sin²θ( cosec²θ - 1 )

= sin²θ( 1/sin²θ - 1 )                                            [Since cosecθ = 1/sinθ]

= sin²θ[ (1 - sin²θ) /sin²θ ]

= sin²θ[ (cos²θ) /sin²θ ]                                       [Since cos²θ + sin²θ = 1]

= cos²θ.

The answer is B.

2)

secθ( 1 - sin²θ )

= secθ( cos²θ )                                                    [Since cos²θ + sin²θ = 1]

= 1/cosθ ( cos²θ )                                                [Since secθ = 1/cosθ]  

= cosθ.

The answer is B.