Question

plz answer my question ​

Answer 1

1.⠀|| ☆.Question.☆ ||

Find the value of ( Sin² A - 1)( Cosec²(90° -A ) .

⠀|| ☆.Solution.☆ ||

( Sin² A - 1)( Cosec²(90° -A )

= -( 1 - Sin² A )( Cosec²(90° - A )

= - ( Cos² A ) ( Sec² A )

= - ( Cos A Sec A )²

= - ( 1 ) ²

= -1 .

______________________

Using Identity

★ ( 1 - Sin² x ) = cos² x

★ ( Cosec 90° - x ) = Sec x

★ Sec x = 1/Cos x

★ ( Cos x )×(Sec x ) = 1

______________________

2. || ☆.Question.☆ ||

If the arithmetic mean of 5, 8, 6, 7, x, and 4 is 6 then find the value of x ?

|| ☆.Solution.☆ ||

A/c to question,

( mean of 5, 8, 6, 7, x, and 4 is 6 )

➥ ( 5 + 8 + 6 + 7 + x + 4 )/6 = 6

➥ (30 + x)/6 = 6

➥ 30 + x = 6 × 6

➥ x = 36 - 30

➥ x = 6 Ans.

______________________

Verification of second answer:-

______________________

( mean of 5, 8, 6, 7, x = 6, and 4 is 6 )

➥ ( 5 + 8 + 6 + 7 + 6 + 4 )/6 = 6

➥ ( 36)/6 = 6

➥ 6 = 6

L.H.S. = R.H.S.

That's Proved

______________________

Thus:-

• Answer of first question will be options number (A) .
• Answer of second question will be options number (B)

__________________

Answer 2

${\huge{\mathbb{\red{1.}}}}$

${\red{\underline{\bf{To\:find\::}}}}$

$\mathtt{(\:Sin^2\:A\:-\:1)(\:Cosec^2(90°\:-A\:)\&=\:?}$.

${\red{\underline{\bf{Answer\::}}}}$

$\bf{A.\:-1}$

${\red{\underline{\mathtt{Solution}}}}$

( Sin² A - 1)( Cosec²(90° -A )

➙ -( 1 - Sin² A )( Cosec²(90° - A )

➙ - ( Cos² A ) ( Sec² A )

➙ - ( Cos A Sec A )²

➙ - ( 1 ) ²

➙ $\bf\pink{-1}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\underline{\mathfrak{\green{Identity\:used}}}}$

• ( 1 - Sin² x ) = cos² x

• ( Cosec 90° - x ) = Sec x

• Sec x = 1/Cos x

• ( Cos x )×(Sec x ) = 1

_______________________________

${\huge{\mathbb{\red{2.}}}}$

${\red{\underline{\bf{Given\::}}}}$

$\mathtt{Arithmetic\:mean\:of\:5,\:8,\:6,\:7,\:x\:and\:4\:=\:6}$

${\red{\underline{\bf{To\:find\::}}}}$

$\mathtt{x\:=\:?}$

${\red{\underline{\bf{Answer\::}}}}$

${\underline{\mathfrak{\green{As\:given\:,}}}}$

( mean of 5, 8, 6, 7, x, and 4 is 6 )

${\underline{\mathfrak{\green{So\:,}}}}$

➙ ( 5 + 8 + 6 + 7 + x + 4 )/6 = 6

➙ (30 + x)/6 = 6

➙ 30 + x = 6 × 6

➙ x = 36 - 30

➙ $\bf\pink{x\:=\:6\:}$