Question

sin∅-cos∅=0 prove sec∅=root 2 of trignometric question

Answer 1

GIVEN:

sin ∅ - cos ∅ = 0

TO PROVE:

sec ∅ = √2

FORMULAE:

tan ∅ = sin ∅ / cos ∅

1 = tan 45°

sec 45° = √2

PROOF:

sin ∅ - cos ∅ = 0

sin ∅ = cos ∅

tan ∅ = 1

1 = tan 45°

∅ = 45°

sec ∅ => sec 45° = √2

HENCE PROVED.

SOME MORE FORMUALE REALTED TO sec ∅

sec ∅ = $\sqrt{1 + tan^2 \phi}$

sec ∅ = tan ∅ × cosec ∅

sec ∅ = 1 / cos ∅

sec ∅ = cosec(90° - ∅)

Answer 2

Answer:

If cos θ + sin θ = √2 cos θ prove that cos θ - sin θ = √2 sin θ.

1 vote

Let θ = x cos x + sin x = √2 cos x squaring on both side, we get...... cos2x + sin2x + 2cosxsinx = 2cos2x 2sinxcosx = 2cos2x - cos2x - sin2x 2sinxcosx ...