sintheeta +costheeta /sinetheta-costheta + sin thetha-costheta /sinetheta+costheta =2secsquaretheta /tansquare-1
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given sinα -cosα /sinα +cosα +sin α +cosα/sin α -cos α =2/2sin²-1
L.H.S.
take lcm
⇒[( sinα -cosα)²+ ( sinα +cosα)²]/[( sinα -cosα)( sinα +cosα)]
⇒2(sin²α+cos²α) /(sin²α-cos²α) [ ∵ (a+b)²+(a-b)²= 2(a²+b²)]
⇒2/(cos 2α) [ ∵ sin²α-cos²α=cos 2α]
⇒2/ 2sin²α-1 [ ∵ cos 2α= 2sin²α-1 ]
L.H.S.=R.H.S.
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