CameraIcon

SearchIcon

MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Range of Trigonometric Ratios from 0 to 90 Degrees

If asin∅+b co...

Question

If asinø+bcosø=c then prove that acosø-bsinø=(a²+b²-c²)^-1

Open in App

Solution

asinΦ+bcosΦ=c

Squaring both sides

a²sin²Φ + b²cos²Φ+2absinΦcosΦ=c²

a²(1-cos²Φ)+b²(1-sin²Φ)+2absinΦcosΦ=c²

a²-a²cos²Φ+b²-b²sin²Φ+2abcosΦsinΦ=c²

a²+b²-c²=(acosΦ-bsinΦ)²

Suggest Corrections

thumbs-up

6

Similar questions

a cos θ + b sin θ = c

, then prove that:

a sin θ - b cos θ = \pm \sqrt{a^{2} + b^{2} - c^{2}}

x = a sin θ + b cos θ

y = a cos θ - b sin θ

, then prove that

x^{2} + y^{2} = a^{2} + b^{2}

a cos θ - b sin θ = c

α sin θ + b cos θ = \pm \sqrt{a^{2} + b^{2} - c^{2}}

a cos θ + b sin θ = p

a sin θ - b cos θ = q

a^{2} + b^{2} = p^{2} + q^{2}

a cos θ - b sin θ = c

(a sin θ + b cos θ) - \sqrt{(a^{2} + b^{2} - c^{2})}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Range of Trigonometric Ratios from 0 to 90

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Range of Trigonometric Ratios from 0 to 90 Degrees

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon