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निम्नलिखित सर्वसमिकाओं को सिद्ध कीजिए। ...

निम्नलिखित सर्वसमिकाओं को सिद्ध कीजिए।
`(sin theta+cos theta)/(sin theta-cos theta)+(sin theta-cos theta)/(sin theta+cos theta)=(2)/(1-2cos^(2) theta)`

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(sin theta-cos theta)/(sin theta+cos theta)+(sin theta+cos theta)/(sin theta-cos theta)=(2)/((2sin^(2)theta-1))

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

(sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)

cos theta+sin theta=cos2 theta+sin2 theta

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

Prove that (1+cos theta)/(sin theta)=(1+sin theta+cos theta)/(1+sin theta-cos theta) .

3. sin^(3)theta+cos^(3)theta=(sin theta+cos theta)(1-sin theta cos theta)

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

(cos theta)/(1-sin theta)=(1+cos theta+sin theta)/(1+cos theta-sin theta)