Question

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Please answer this question in the above image ​

Answer 1

Answer:

65/8

Step-by-step explanation:

' theta ' is written as ' A '

24sin² A + 15cos² A = 16

Using trigonometric identity cos² A = 1 - sin² A

⇒ 24sin² A + 15( 1 - sin² A ) = 16

⇒ 24sin² A + 15 - 15sin² A = 16

⇒ 9sin² A = 16 - 15

⇒ 9sin² A = 1

⇒ sin² A = 1 / 9

We know that

cos² A = 1 - sin² A

⇒ cos² A = 1 - 1/9

⇒ cos² A = ( 9 - 1 )/9

⇒ cos² A = 8/9

• tan² A = sin² A / cos² A = ( 1 / 9 ) ÷ ( 8 / 9 ) = 1 / 8

• cot² A = 1 / tan² A = 1 ÷ ( 1 / 8 ) = 8

Now let's find the value of tan² A + cot² A

tan² A + cot² A

= 1/8 + 8

= ( 1 + 64 ) / 8

= 65 / 8

Therefore the value of tan² A + cot² A is 65/8.

Answer 2

Step-by-step explanation:

Hope it helps you :)

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