Question

Sin square theta divided by cos square theta + cos square theta divided by sin square theta = secant square theta - cosecant square theta - 2

Answer 1

hey view the following attachment for solution

Answer 2

Answer:

Sin²a/Cos²a  +  Cos²a/Sin²a = Cosec²a + Sec²a - 2

Step-by-step explanation:

Using a instead of thetha

Sin²a/Cos²a  +  Cos²a/Sin²a

= (Sin^4a + Cos^4a)/(Cos²a.Sin²a)

as we know x² + y² = ( x+y)² - 2xy

here x = Sin²a  & y = Cos²a

= ( (Sin²a + Cos²a)² - 2Sin²a.Cos²a)/(Cos²a.Sin²a)

=  (1 - 2Sin²a.Cos²a)/(Cos²a.Sin²a)

= 1/(Cos²a.Sin²a)  - 2

1 =  Cos²a + Sin²a

= (Cos²a + Sin²a)/(Cos²a.Sin²a)   - 2

= Cos²a/(Cos²a.Sin²a)    + Sin²a/(Cos²a.Sin²a)     - 2

= 1/Sin²a  + 1/Cos²a  - 2

= Cosec²a + Sec²a - 2

= Sec²a + Cosec²a - 2

looks like in question - Cosec² is by mistake