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Sveta_85 [38]
3 years ago
11

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

Mathematics
2 answers:
AleksAgata [21]3 years ago
5 0

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

guajiro [1.7K]3 years ago
3 0

Answer:

\huge\mathcal\colorbox{red}{\color{pink}{ᶛɲƧཡэʀ}}

  • Manipulating left side

2csc (2x)

  • Express with sin, cos

2/sin (2x)

  • Rewrite using trig identities

<em><u>1/ cos(x) sin(x)........(1)</u></em>

  • Manipulating right side

1+ tan²(x)/tan(x)

  • Express with sin, cos

cos²(x) + sin²(x) /cos(x) sin(x)

  • Rewrite using trig identities

<em><u>1/cos(x) sin(x)....... ( 2)</u></em>

From 1st& 2nd ,we get

<em><u>LHS=</u></em><em><u> </u></em><em><u>RHS</u></em>

<em><u>Hence,</u></em><em><u> </u></em><em><u>Proved</u></em><em><u> </u></em><em><u>✓</u></em>

<em><u>\\  \\</u></em>

<em><u>~ʆᵒŕ∂ཇꜱꜹⱽẻⱮë</u></em>

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