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Question

Prove that : tan1[6x8x3112x2]tan1[4x14x2]=tan12x,|2x|<13

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Solution

tan1[6x8x3112x2]tan1[4x14x2]=tan12x,|2x|<13
On solving LHS we get tan1atan1b=tan1(ab1+ab)
tan1[6x8x3112x2]tan1[4x14x2]=tan1[6x8x3112x24x14x2]
1+(6x8x3)(4x)(112x2)(14x2)
tan1[6x24x38x3+32x54x+48x314x212x2+48x4+24x232x4]
tan1[32x5+16x3+2x16x4+8x2+1]
tan1[2x[16x4+8x2+1]16x4+8x2+1]
tan1(2x)=RHS
Hence proved.

1182975_1356929_ans_56e24d565001455ea7b7d7fbc6c2ac40.jpg

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