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If cos theta + sintheta = sqrt2 cos thet...

If `cos theta + sintheta = sqrt2 cos theta`; show that `costheta- sintheta = sqrt2 sintheta`

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We have
` cos theta + sin theta = sqrt(2) cos theta `
` rArr (cos theta + sin theta)^(2) = 2cos^(2)theta `
` rArr cos^(2)theta + sin^(2)theta + 2cos theta sin theta = 2 cos^(2)theta `
`rArr cos^(2)theta - 2cos theta sin theta = sin^(2)theta `
`rArr cos^(2)theta - 2cos theta sin theta + sin^(2)theta = sin^(2)theta + sin^(2)theta `
[adding `sin^(2)theta` on both sides]
` rArr (cos theta - sin theta)^(2) = 2sin^(2)theta `
` (cos theta - sin theta)= sqrt(2)sin theta . `
Hence, `(cos theta - sin theta)=sqrt(2)sin theta . `
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Test Yourself
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  4. If cosA+cos^(2)A=1, then sin^(2)A+sin^(4)A=?.

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  5. If sin theta=(sqrt(3))/(2)" then " ("cosec"theta+cot theta)=?

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  6. If cotA=(4)/(5), then ((sinA+cosA))/((sinA-cosA))=?

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  7. If 2x=secA and (2)/(x)=tanA, " prove that " (x^(2)-(1)/(x^(2)))=(1)/(4...

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  10. If 2sin2 theta=sqrt(3) ,then the value of theta is :

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  11. Prove that sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).

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  12. If cosec theta + cot theta= p, cos theta = ?

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  13. Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

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  14. If 5cottheta=3. find the value of (5sintheta-3costheta)/(4sintheta+3co...

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  15. Prove that (sin32^(@)cos58^(@)+cos32^(@)sin58^(@))=1.

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  16. If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove t...

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  17. ((1+sintheta))/((1-sintheta))=?

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  18. Prove that (1)/((sec theta - tan theta))-(1)/(cos theta)=(1)/(cos th...

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  19. ((sinA-2sin^(3)A))/((2cos^(3)A-cosA)) = ?

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  20. Prove that (tanA)/((1-cotA))+(cotA)/((1-tanA))=(1+tanA+cotA).

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