Question

If sin A = cos A, find the value of 2 tan²A - 2 sec² A + 5.

Answer 1

Consider the figure : 

sin A = cos A

tan A = `(1)/(1)`

i.e.`"perpendicular"/"base" = "BC"/"AB" = (1)/(1)`

Therefore if length of perpendicular = x, length of base = x

Since
AB² + BC² = AC²  ...[ Using Pythagoras Theorem]

(x)² + (x)² = AC²

AC² = 2x²

∴ AC = `sqrt2x`

Now

sec A = `"AC"/"AB" = sqrt2`

Therefore
2 tan² A – 2sec² A + 5

= 2(1)² –2 (`sqrt2`)² + 5

= 2 – 4 + 5

= 3