Let x = \θ + \θ and y = \θ - \θ for an acute angle \θ . Which relation between x and y holds?

Question

Accepted Answer

x^2 - y^2 = 4√xy. x^2 - y^2 = (x + y)(x - y) = (2 \θ)(2 \θ) = 4 \θ \θ . Also xy = ^2\θ - ^2\θ = ^2\θ(1 - ^2\θ)/ ^2\θ = ^4\θ/ ^2\θ , so √xy = ^2\θ/ \θ = \θ \θ . Hence x^2 - y^2 = 4√xy . Using x^2 + y^2 loses the neat product, since that sum is 2 ^2\θ + 2 ^2\θ ; using the factor 2 instead of 4 forgets one of the two doubles.

Let $x = tan θ + sin θ$ and $y = tan θ - sin θ$ for an acute angle $θ$ .
Which relation between $x$ and $y$ holds?

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More Class 10 Trigonometric Identities practice

Let x=tanθ+sinθ and y=tanθ−sinθ for an acute angle θ.Which relation between x and y holds?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Trigonometric Identities practice

Let $x = tan θ + sin θ$ and $y = tan θ - sin θ$ for an acute angle $θ$ .
Which relation between $x$ and $y$ holds?