Question

If cosA + secA = 2 prove cos⁴A + sec⁴A = 2.​

Answer 1

Explanation:

cos A+secA=2

squaring

cos²A+sec²A+2cosA sec A=4

cos²A+sec²A+2cos A/cos A=4

cos²A+sec²A+2=4

cos²A+se²A=4-2=2

again squaring

cos^4A+sec^4A+2cos²Asec²A=4

cos^4A+sec^4A+2=4

cos^4A+sec^4A=4-2=2