Question

Find the value of:

(2 cos 0° + sin 45°)(tan 45° − cos 45° + sin 90°)

Answer 1

Given:

(2 cos 0° + sin 45°)(tan 45° − cos 45° + sin 90°)

Step 1: Use standard trigonometric values

cos 0° = 1

sin⁡ 45° = `1/sqrt2`

tan⁡ 45° = 1

cos 45° = `1/sqrt2`

sin⁡ 90° = 1

Step 2: Substitute values

2 cos 0° + sin 45° = 2(1)  + `1/sqrt2 = 2 + 1/sqrt2` 

tan 45° − cos 45° + sin 90° = 1 − `1/sqrt2 + 1 = 2 − 1/sqrt2` 

Step 3: Multiply both expressions

`(2 + 1/sqrt2) (2 − 1/sqrt2)`

(a + b) (a − b) = a² − b²

`(2)^2 − (1/sqrt2)^2 = 4 − 1/2 = 3.5`

3.5 = `3 1/2`