Question

Prove that
Tan theta + cot theta + 2 = sec square theta. Cosec square theta ​

Answer 1

Answer:

Step-by-step explanation:

Solution :

2. i think that u have made a little mistake in wrting the question.... the question should be right is this way
4. prove that tan2 theta+cot2 theta + 1 = 2 cosec2 theta* sec square theta?
5. Now by solving according to right ques:
6. Taking L.H.S:
7. as tan theta = sin theta divided by cos theta and cot theta is inverse of tan theta
9. by breaking tan square and cot square theta into their respective formulas
10. sin2 theta divided by cos2 theta + cos2 theta divided by sin2 theta
11. Now by taking L.C.M  
13. sin2 theta + cos2 theta  +1              1+1           as sin2 theta + cos2 theta= 1
14. -----------------------------          =    ---------------
15. (cos2 theta) (sin2 theta)             (cos2 theta) ( sin2theta)
17.       2
18. ----- ---------    
19. (cos2 theta) ( sin2teta)
21. as sec2theta = 1                       and              cosec2theta = 1            
22.                        ------                                                        ----------
23.                         cos2theta                                                sin2theta
25. so 2  ( 1 divided by cos2theta) = 2 sec square  theta
26. and 2  ( 1 divided by sin2 theta ) = 2 cosec square theta
29. L.H.S = R.H.S  
30. Hence prooved...

Answer 2

Answer:

I have answered below for the following question :

tan²θ+ cot²θ  + 2 = sec²θ x cosec²θ