Question

Prove that sec⁴θ ( 1- sin⁴θ) - 2 tan²θ = 1


CLASS 10TH CBSE SAMPLE PAPER

Answer 1

hope it helpful !!!!!

Answer 2

Hello!!
_____________________________________________________________

Here is ur answer :-


L.H.S. = sec ⁴θ (1 - sin⁴θ) - 2 tan²θ
 = sec⁴θ - sec⁴θsin⁴θ - 2tan²θ 
= sec⁴θ - sinθ⁴/cos⁴θ - 2tan²θ 
= sec⁴θ - tan⁴θ - 2tan²θ
= (sec²θ + tan²θ) (sec²θ - tan²θ) - - 2tan²θ[a² - b² = (a + b)(a - b)] [ Using identity  of tan²θ + 1 = sec²θ ] 

= (sec²θ + tan²θ) (1) - 2tan²θ 
= sec²θ - tan²θ 
=) 1 = RHS  [Using identity of tan²θ + 1 = sec²θ]
           
                 HENCE PROVED!!