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If cos theta-sin theta=sqrt(2)cos theta,...

If `cos theta-sin theta=sqrt(2)cos theta`, then prove that `cos theta+sin theta=pm sqrt(2) sin theta`.

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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. If 3 sin theta+4 cos theta=5, then prove that sin theta=(3)/(5).

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  2. If sin theta+"cosec"theta=2, then prove that sin^(7) theta+"cosec"^(7)...

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  3. If cos theta-sin theta=sqrt(2)cos theta, then prove that cos theta+sin...

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  4. If (a^(2)-b^(2))sin theta+2 ab cos theta-(a^(2)+b^(2))=0, then prove t...

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  5. Prove that tan theta+sqrt((1-sintheta)/(1+sin theta))=sec theta.

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  6. Prove that (tan theta+sec theta)^(2)=(1+sin theta)/(1-sin theta).

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  7. Prove that (tan theta)/(sec theta-1)+(tan theta)/(sec theta+1)=2 "cose...

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  8. Prove that sqrt((1+costheta)/(1-costheta))+sqrt((1-cos theta)/(1+cos ...

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  9. Prove that (sin A+sinB)/(cosB-cosA)=(cos A+cosB)/(sinA-sinB).

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  10. Prove that (sec theta-tan theta+1)/(sec theta+tan theta+1)=(1-sin the...

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  11. Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha...

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  12. If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3), then ...

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  13. eliminate theta : a(1) sec theta + b(1)tan theta+c(1)=0 , a(2)sec thet...

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  14. If tan theta=(a)/(b) , then find the value of (sin theta)/(cos^(8)thet...

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  15. If a^(2)sec^(2)alpha-b^(2)tan^(2)alpha=c^(2), then prove that sinalpha...

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  16. If tan theta=k, then show that sec theta+tan^(3)theta "cosec"theta=(1...

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  17. If tan^(2)theta=1-e^(2), then prove that sectheta+tan^(3)theta"cosec...

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  18. If " cosec"theta-sin theta=m and sec theta-cos theta=n, then prove tha...

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  19. If a sin x=b cosx=(2c tan x)/(1-tan^(2)x), then prove that (a^(2)-b^(...

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  20. If (sin alpha-cosalpha)/(sin alpha+cosalpha)=tan theta, then prove tha...

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