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Prove that: sqrt((sectheta-1)/(sectheta+...

Prove that: `sqrt((sectheta-1)/(sectheta+1))+sqrt((sectheta+1)/(sectheta-1))=2\ cos e c\ theta`

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We have
`LHS = sqrt((sec theta -1)/(sec theta +1)) + sqrt((sec theta +1)/(sec theta -1))= (sqrt(sec theta -1))/(sqrt(sec theta +1)) + (sqrt(sec theta +1))/(sqrt(sec theta -1)) `
` = (sec theta -1+ sec theta +1)/(sqrt((sec theta +1)(sec theta -1))) =(2 sec theta)/(sqrt(sec^(2)theta -1))=(2sec theta)/(tan theta) " "[ because sec^(2)theta -1= tan^(2)theta] `
`= 2 sec theta cot theta = (2)/(cos theta) xx (cos theta)/(sin theta)=(2)/(sin theta) = 2 "cosec" theta = RHS.`
` therefore LHS = RHS. `
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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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  8. If sqrt(3) tantheta=3sintheta, " prove that " (sin^(2)theta-cos^(2)the...

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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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  21. If sec5A="cosec"(A-36^(@)) and 5A " is an acute angle, show that " A=2...

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