Question

(1 + tan theta + sec theta)(1+cot theta - cosec theta)

Answer 1

Answer:

2

Explanation:

(1 + cos/sin - 1/sin ) (1+1/cos + sin /cos )

( cos + sin - 1) (cos + sin +1 )

---------------------------------------

cos  * sin

(cos+sin)² - 1²

-----------------

cos * sin

1+ 2 cos sin - 1

-----------------

cos*sin

2

Answer 2

Answer:2

Explanation:

For my convenience let the angle be A

(1+tanA+secA)(1+cotA-cosecA)

TanA=sin/cos

Sec=1/cos

closed=1/sin

So,(1+sinA/cos+1/cosA)(1+cosA/sinA-1/sinA)

[(cosA+sinA)+1]/cosA * [(sinA+cosA)-1]/sinA

[(cosA+sinA)2-1]/cosAsinA

(1+2sinAcosA-1)/cosAsinA

2sinAcosA/sinAcosA

=2