Question

pls answer it I want perfect answer no spam .........​

Answer 1

sin15=0.25

cos15=0.96

tan45=1

Answer 2

Answer:

2 - √3

Step-by-step explanation:

Let t be the value of the expression.

Since tan 45° = 1,

t = ( sin 15° ) / ( cos 15° ) = tan 15°.

Since 0° < 15° < 45°, we know that 0 < t < 1.

By compound angle formula for tan 2x,

tan 30° = 2 tan 15° / ( 1 - tan² 15° )  =  2t / ( 1 - t² ).      ... (*)

By compound angle formula for tan (x+y),

tan 45° = tan ( 15° + 30° ) = ( tan 15° + tan 30° ) / ( 1 - tan 15° tan 30° )

=> 1 = ( t + tan 30° ) / ( 1 - t tan 30 )

=> 1 - t tan 30° = t + tan 30°

=> 1 - 2t²/(1-t²) = t + 2t/(1-t²)                   [ by equation (*) ]

=> ( 1 - t² ) - 2t² = t ( 1 - t² ) + 2t                 [ multiply by (1-t²) ]

=> ( 1 - t² ) - t ( 1 - t² ) - 2t² - 2t = 0

=> ( 1 - t ) ( 1 - t² ) - 2t ( 1 + t ) = 0

=> ( 1 - t )² ( 1 + t ) - 2t ( 1 + t ) = 0

=> ( 1 - t )² - 2t = 0                               [ can divide by 1+t since t ≠ -1 ]

=> t² - 4t + 1 = 0

=> t = ( 4 ± √(4² - 4) ) / 2  =  ( 4 ± √12 ) / 2  =  2 ± √3.

=> t = 2 - √3                                    [ since 0 < t < 1 ].