Question

sec⁴ A − sec² A is equal to
(a)tan² A − tan⁴ A
(b)tan⁴ A − tan² A
(c)tan⁴ A + tan² A
(d)tan² A + tan⁴ A

Answer 1

Answer:

sec⁴ A − sec² A is equal to (tan²A + tan⁴A)  

Among the given options option (d) (tan²A + tan⁴A)  is correct.

Step-by-step explanation:

Given : sec⁴ A − sec² A

sec⁴ A − sec² A

= sec²A(sec²A - 1)

[Taking sec²A common]

= (1 + tan²A) × tan²A  

[∵ sec²θ = 1 + tan²θ & sec²θ - 1 = tan²θ ]

sec⁴ A − sec² A  =  (tan²A + tan⁴A)  

Hence, sec⁴ A − sec² A is equal to (tan²A + tan⁴A)  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

SOLUTION

L.H.S

${sec}^{4}A - {sec}^{2} A \\ \\ = > {sec}^{2} A( {sec}^{2} A - 1) = (1 + {tan}^{2} A)[(1 + tan {}^{2} A) - 1]\\ \\ = > (1 + {tan}^{2} A)( {tan}^{2} A) = {tan}^{2} A + {tan}^{4} A \\ so \\ = > {sec}^{4} A - {sec}^{2} A = {tan}^{4} A + {tan}^{2} A$

R.H.S

hence proved ☺️