0

Guest

Courses New

Prove that Sec^4(1-sin^4)-2tan^2=1 using trigonometric identity

Prove that Sec^4(1-sin^4)-2tan^2=1 using trigonometric identity

Grade:10

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
sec⁴A(1-sin⁴A)-2tan²A
=sec⁴A-sec⁴Asin⁴A-2tan²A
=sec⁴A-sin⁴A(1/cos⁴A)-2tan²A
=sec⁴A-tan⁴A-2tan²A
={(sec²A)²-(tan²A)²}-2tan²A
=(sec²A+tan²A)(sec²A-tan²A)-2tan²A
=sec²A+tan²A-2tan²A [∵, sec²A-tan²A=1]
=sec²A-tan²A
=1 (Proved)
 
Regards
Arun (askIITians fpoum expert)

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More