Prove that, tan70 =tan20+2tan50 2 . Prove that, (sinX) 3 × sin3X +(cosX) 3 × cos3X =(cos2X) 3

Question

Prove that, tan70 =tan20+2tan50 2 . Prove that, (sinX) 3 × sin3X +(cosX) 3 × cos3X =(cos2X) 3

Anish Singhal · Answer

According to the trigonometric identity,
tan70=tan(20+50)
tan70=(tan20+tan50)/1-tan20tan50
tan70-tan20tan50tan70=tan20+tan50
Also tan70tan20=tan70cot70=1
Hence
tan70-tan50=tan20+tan50
So tan70=tan20+2tan50

Saurabh Koranglekar · Answer

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Prove that, tan70 =tan20+2tan50 2 . Prove that, (sinX) 3 × sin3X +(cosX) 3 × cos3X =(cos2X) 3

Prove that, tan70 =tan20+2tan50
2 . Prove that,
(sinX)³× sin3X +(cosX)³ × cos3X =(cos2X)³

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Prove that, tan70 =tan20+2tan50 2 . Prove that, (sinX) 3 × sin3X +(cosX) 3 × cos3X =(cos2X) 3

Prove that, tan70 =tan20+2tan50 2 . Prove that,(sinX)3 × sin3X +(cosX)3 × cos3X =(cos2X)3

2 Answers

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Prove that, tan70 =tan20+2tan50
2 . Prove that,
(sinX)³× sin3X +(cosX)³ × cos3X =(cos2X)³