Math, asked by ramadevipujagmail, 9 months ago

If 1/sin +1/tan =9,then find the value of cot -cosec? with explanation ​

Answers

Answered by Anonymous
0

Step-by-step explanation:

HERE IS YOUR ANSWER

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take LCM

WE GET

here \: it \: is \: given \: that \:  \\  \cot( \alpha )  +  \csc( \alpha )  = 9 \\  \\ and \: we \: know \: that \:  \\  \\   { \csc( \alpha ) }^{2}  -  { \cot( \alpha ) }^{2}  = 1 \\  \\  \\  \\  \\ so \: required \: answer \:  =  \frac{1}{9}

Answered by tahseen619
4

 -  \dfrac{1}{9}

Step-by-step explanation:

Given:

 \dfrac{1}{ \sin }  +  \dfrac{1}{ \tan }  = 9

To find:

 \cot -  \cosec

Solution:

 \dfrac{1}{ \sin }  +  \dfrac{1}{ \tan }  = 9 \\ \\  ⟹  \cosec +   \cot \:  = 9 \:  \:  \: .......(i)

As We know,

 { \cosec}^{2}  -  \cot {}^{2}  = 1 \\  \\  ⟹ ({ \cosec}^{}   +   \cot {}^{})({ \cosec}^{}  -  \cot {}^{}) = 1 \\  \\ ⟹9({ \cosec}^{}  -  \cot {}^{}) = 1 \:  \:  \:  \:  \:  [ \:  From \:  \:  i ]  \\ \\⟹ ({ \cosec}^{}  -  \cot {}^{}) =  \frac{1}{9}  \\  \\ ⟹- ({ \cosec}^{}  -  \cot {}^{}) =  -  \frac{1}{9}  \\  \\⟹ \cot {}^{}{ -  \cosec}^{}   = -   \frac{1}{9}

Hence, the required answer is - 1/9 .

Some important trigonometry Rules:

sinø . cosecø = 1

cosø . secø = 1

tanø . cotø = 1

sin²ø + cos²ø = 1

cosec²ø - cot² = 1

sec²ø - tan²ø = 1

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