Question

URGENT PLEASE HELP SERIOUS ANSWERS ONLY verify 2 csc (2x)=1+ tan^2 x / tan x

Answer 1

Step-by-step explanation:

L.H.s.

• 2csc2x
• 2/sin2x
• 2/(2sinxcosx)
• 1/sinxcosx
• [sin²x+cos²x]/sinxcosx
• sin x/cosx +cosx/sinx
• tanx+cotx

R.H.S.

• 1+ tan²x/tanx
• 1+tanx
• 1+sin x/cosx
• (cosx+sinx)/cosx

Answer 2

Answer:

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• Manipulating left side

2csc (2x)

• Express with sin, cos

2/sin (2x)

• Rewrite using trig identities

1/ cos(x) sin(x)........(1)

• Manipulating right side

1+ tan²(x)/tan(x)

• Express with sin, cos

cos²(x) + sin²(x) /cos(x) sin(x)

• Rewrite using trig identities

1/cos(x) sin(x)....... ( 2)

From 1st& 2nd ,we get

LHS= RHS

Hence, Proved ✓

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