Question

yadi sec 4A= cosec(A-20 °) jahan 4A ek nyun kond hai, to dikhayie ki sin[B+C]/2= cosA/2

Answer 1

sec 4A= cosec(A-20 °)

cosec ( 90 - 4A ) = cosec ( A - 20°)

90 - 4A = A - 20

90 + 20 = A + 4A

110 = 5A

A = 110/5 = 22°

A + B + C = 180° ( Angle sum property)

B + C = 180 - A

Apply sin on both sides

sin ( B + C) = sin (180 - A)

Divide by two on both sides

Sin ( B + C ) /2 = sin ( 180 - A)/2
Sin ( B + C ) /2 = sin (90 - A)/2
Sin ( B + C ) /2 = cos A /2

Hence proved
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Answer 2

Answer:

Sec 4A = Cosec ( A-20 )

Sec ( 90 - 4A ) = Cosec ( A - 20 )

Cosec ( 90 - 4A ) = Cosec ( A - 20 )

Cosec cosec cancel..

90 - 4 A = A - 20

- 4 A - A = - 20 - 90

- - = + then,

5 A = 110

A = 110/5

A = 22

Sin[B + C/2] = Cos A/2

Step-by-step explanation:

As we know,

< this sign for angle..

<A + <B + <C = 180

<B + <C = 180 - <A

<B + <C/2 = 180 - <A/2

= 180/2 - <A/2

= 90 - <A/2

L.H.S = Sin [ B + C /2 ]

= Sin [ 90 - <A/2 ]

= Cos <A/2

L.H.S = R.H.S

Hope! its help u......