Question

(1 – Cot 200°)(1 – Cot 25°) =​

Answer 1

Answer:

$\Large{ \bf{ \red{\mathfrak{SOLUTION}}}}$

(1 – Cot 200°)(1 – Cot 25°)

$\frac{( sin200° - cos200°)(sin25° - cos25°)}{ \sin(200°). \sin(25°) }$

$= > \frac{( \sin200° + \sin110°) ( \sin25° - \sin65°) }{sin200°. \sin25°) }$

$= > ({{ \frac{2sin(200 + 110)}{2}. \frac{ \cos(200 - 110) }{2} }})( \frac{2 \cos(25 + 65) }{2} . \frac{ \sin(65 - 25) }{2} ) / \sin(200) \sin(25)$

$= > \frac{ - 4(sin155°.cos45°)(cos45°.sin20°)}{ \sin(180 + 20).sin25° }$

$= > \frac{ - 4 \times (sin45 \times cos45)sin(180 - 25).sin20°}{( - sin20°)(sin25°}$

$= > 4 \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } . \frac{sin25°.sin20°}{sin20°.sin25°}$

$= > 4 \times \frac{1}{2} = 2$

$Therefore , \: \: \pink 2 \: \: \: is \: the \: \: answer$

______________________

Answer 2

Step-by-step explanation:

(1 – Cot 200°)(1 – Cot 25°)

\begin{gathered}\frac{( sin200° - cos200°)(sin25° - cos25°)}{ \sin(200°). \sin(25°) } \\ \end{gathered}

sin(200°).sin(25°)

(sin200°−cos200°)(sin25°−cos25°)

\begin{gathered} = > \frac{( \sin200° + \sin110°) ( \sin25° - \sin65°) }{sin200°. \sin25°) } \\ \end{gathered}

=>

sin200°.sin25°)

(sin200°+sin110°)(sin25°−sin65°)

\begin{gathered} = > ({{ \frac{2sin(200 + 110)}{2}. \frac{ \cos(200 - 110) }{2} }})( \frac{2 \cos(25 + 65) }{2} . \frac{ \sin(65 - 25) }{2} ) / \sin(200) \sin(25) \\ \end{gathered}

=>(

2

2sin(200+110)

.

2

cos(200−110)

)(

2

2cos(25+65)

.

2

sin(65−25)

)/sin(200)sin(25)

\begin{gathered} = > \frac{ - 4(sin155°.cos45°)(cos45°.sin20°)}{ \sin(180 + 20).sin25° } \\ \end{gathered}

=>

sin(180+20).sin25°

−4(sin155°.cos45°)(cos45°.sin20°)

\begin{gathered} = > \frac{ - 4 \times (sin45 \times cos45)sin(180 - 25).sin20°}{( - sin20°)(sin25°} \\ \end{gathered}

=>

(−sin20°)(sin25°

−4×(sin45×cos45)sin(180−25).sin20°

\begin{gathered} = > 4 \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } . \frac{sin25°.sin20°}{sin20°.sin25°} \\ \end{gathered}

=>4×

2

1

×

2

1

.

sin20°.sin25°

sin25°.sin20°

\begin{gathered} = > 4 \times \frac{1}{2} = 2 \\ \end{gathered}

=>4×

2

1

=2

Therefore , \: \: \pink 2 \: \: \: is \: the \: \: answerTherefore,2istheanswer

______________________