Question

what is the value of tan²theta - sec²theta by cot²theta - cosec²theta​

Answer 1

Answer:

answer is 1

Step-by-step explanation:

Step 1 : There is a formula which shows relation between tanФ and secФ as shown below,

1 + $tan^{2}$Ф = $sec^{2}$Ф.

Step 2 : Change the side of $sec^{2}$Ф from right to left and also change the side for 1 from left to right we get,

$tan^{2}$Ф - $sec^{2}$Ф = -1     (Arrange as per our requirement)

Step 3 : There is a formula which shows relation between cotФ and cosecФ as shown below,

1 + $cot^{2}$Ф = $cosec^{2}$Ф.    

Step 4 : Change the side of $cosec^{2}$Ф from right to left and also change the side for 1 from left to right we get,

$cot^{2}$Ф - $cosec^{2}$Ф = -1     (Arrange as per our requirement)

Step 5 : now put these value in to our question we get,

$tan^{2}$Ф - $sec^{2}$Ф       -1

-------------------  =  -----

$cot^{2}$Ф - $cosec^{2}$Ф     -1

Step 6 :   -1 / -1 will become positive 1.

So the final ans is 1.