Question

sin 70/cos 20 + cosec 20/sec 70- 2cos 70 cosec20 = 0,Prove it.

Answer 1

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Answer 2

Answer:

$\frac{sin70}{cos20}+\frac{cosec20}{sec70}-2cos70cosec20=0$

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Step-by-step explanation:

$LHS = \frac{sin70}{cos20}+\frac{cosec20}{sec70}-2cos70cosec20$

$=\frac{sin(90-20)}{cos20}+\frac{cosec(90-70)}{sec70}-2cos70cosec(90-70)$

$=\frac{cos20}{cos20}+\frac{sec70}{sec70}-2cos70sec70$

$=1+1-2cos70\times \frac{1}{cos70}$

$=1+1-2\\=2-2\\=0\\=RHS$

Therefore,

$\frac{sin70}{cos20}+\frac{cosec20}{sec70}-2cos70cosec20=0$

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