Question

can someone please do this for me

Answer 1

Hello !!

We have,

Sin theta + Cos theta = ✓2 Cos theta

=> ( Sin theta + Cos theta )² = (✓2Cos theta)²

( A + B)² = (A)² + (B)² + 2 × A × B.

=> ( Sin theta + Cos theta)² = 2Cos² theta

=> ( Sin² theta + Cos² theta + 2Cos theta Sin theta = 2Cos² theta .

=> Cos² theta - 2 Cos theta Sin theta = Sin² theta

=> Cos² theta - 2Cos theta Sin theta + Sin² theta = Sin² theta + Sin² theta [ Adding Sin² theta on both sides ]

=> ( Cos theta - Sin theta )² = 2Sin² theta

=> ( Cos theta - Sin theta) = ✓2 Sin theta

=> ✓2 = ( Cos theta - Sin theta )/ Sin theta

=> ✓2 = Cos theta/ Sin theta - Sin theta/Sin theta

=> ✓2 = Cot theta - 1 [ Cos theta/Sin theta = Cot theta ]

=> Cot theta = ✓2 + 1 ....... PROVED ...

★ HOPE IT WILL HELP YOU ★