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Question
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
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Solution
`(b^2 x^2 + a^2 y^2)`
=`b^2 (a sin theta )^2 + a^2 ( bcos theta)^2`
=`b^2 a^2 sin^2 theta + a^2 b^2 cos^2 theta`
=`a^2 b^2 ( sin^2 theta + cos ^2 theta)`
=`a^2 b^2 (1)`
=`a^2 b^2`
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RELATED QUESTIONS
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Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
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Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
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`square/square` = cosec2θ ......[Taking root on the both side]
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and sin θ = `1/("cosec" θ)`
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∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
