Question

If cos square theta - sin square theta = tan square Alfa
then prove that cos square Alfa - sin square Alfa = tan square theta ​

Answer 1

Answer:L.H.S=(tanα+cscβ)  

2

−(cotβ−secα)  

2

 

=tan  

2

α+csc  

2

β+2tanαcscβ−cot  

2

β−sec  

2

α+2cotβsecα

=(tan  

2

α−sec  

2

α)+(csc  

2

β−cot  

2

β)+2tanαcscβ+2cotβsecα

=−1+1+2tanαcscβ+2cotβsecα

=2tanαcotβ(  

sinβ

1

​  

 

cosβ

sinβ

​  

+  

cosα

1

​  

 

sinα

cosα

​  

)

=2tanαcotβ(secβ+cscα)

=R.H.S

Hence proved.

Step-by-step explanation: