If A- B- C are interior angles of a - A B C- show that sec 2B-C-2-1- 2A-2 -3 MARKS-

Concept: 1.5 Marks Application: 1.5 Marks Consider sec^2 ( B+C/2 ) 1 =sec^2 ( 180 A/2 ) 1 =sec^2 ( 180/2 A/2 ) 1 =sec^2 ( 90 A/2 ) 1 =cosec^2 ( A/2 ) 1 ...

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Byju's Answer

Standard IX

Mathematics

Trigonometric Ratios

If A, B, C ar...

Question

If A, B,C are interior angles of a $Δ A B C$ , show that $s e c^{2} (\frac{B + C}{2}) - 1 = c o t^{2} (\frac{A}{2})$ [3 MARKS]

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Solution

Concept: 1.5 Marks
Application: 1.5 Marks

Consider
$s e c^{2} (\frac{B + C}{2}) - 1$

$= s e c^{2} (\frac{180 - A}{2}) - 1$

$= s e c^{2} (\frac{180}{2} - \frac{A}{2}) - 1$

$= s e c^{2} (90 - \frac{A}{2}) - 1$

$= c o s e c^{2} (\frac{A}{2}) - 1$

$= c o t^{2} (\frac{A}{2})$

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Similar questions

Q. If A, B,C are interior angles of a

Δ A B C

, show that

s e c^{2} (\frac{B + C}{2}) - 1 = c o t^{2} (\frac{A}{2})

[3 MARKS]

Q. If

A, B, C

are interior angles of

Δ A B C

, show that :

c o s e c^{2} (\frac{B + C}{2}) - {tan}^{2} \frac{A}{2} = 1

Q. If A, B and C are interior angles of

Δ A B C,

then Prove that :

s i n \frac{(A + C)}{2} = c o s \frac{B}{2} .

If $A, B, C$ are interior angles of $Δ A B C$ then show that, $sin \frac{(B + C)}{2} = cos \frac{A}{2}$

Q. In

A, B, C

are the interior angles of a

Δ A B C

, then show that

sin (\frac{B + C}{2}) = cos (\frac{A}{2})

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If A, B,C are interior angles of a ΔABC, show that sec2(B+C2)−1=cot2(A2) [3 MARKS]

Concept: 1.5 Marks Application: 1.5 Marks Consider sec2(B+C2)−1 =sec2(180−A2)−1 =sec2(1802−A2)−1 =sec2(90−A2)−1 =cosec2(A2)−1 =cot2(A2)

If A, B,C are interior angles of a $Δ A B C$ , show that $s e c^{2} (\frac{B + C}{2}) - 1 = c o t^{2} (\frac{A}{2})$ [3 MARKS]

Concept: 1.5 Marks
Application: 1.5 Marks

Consider
$s e c^{2} (\frac{B + C}{2}) - 1$

$= s e c^{2} (\frac{180 - A}{2}) - 1$

$= s e c^{2} (\frac{180}{2} - \frac{A}{2}) - 1$

$= s e c^{2} (90 - \frac{A}{2}) - 1$

$= c o s e c^{2} (\frac{A}{2}) - 1$

$= c o t^{2} (\frac{A}{2})$