If sinA=cosA, find the value of :

2 tan square A - 2sec square A +5

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Solution

Given

sinA = cos A

sinA/cosA = 1

we know that
sinA/cosA = tan A

hence,

tan A = 1

, but we know that tan 45° = 1

hence,
A = 45°

2tan²A -2sec²A +5

2tan²45° -2sec²45 +5

we know ,

tan²45° = 1 , sec²45° = 2

hence ,

2(1)² - 2 × (√2)² +5

= 2 - 4 +5

= 3

∴ 2tan²A -2Sec²A +5 = 3

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