Question

sin²45°/cos²60°+sin90°/cot60°+cos45°/sin90°=​

Answer 1

Answer:

Hey there!

We know that,

sin30 = 1/2

cos45 = 1/√2

cot45 =1

sec60 = 2

sin60 = √3/2

tan45 = 1

cos30 = √3/2

sin90 = 1 .

sin30°/cos45° + cot45°/sec60° - sin60°/tan45° - cos30°/sin90°

= 1/2 ( 1/√2 ) + 1 / ( 2 ) - (√3/2 ) / ( 1 ) - (√3/2 ) / 1

= (√2 / 2 )+ 1/2+ ( - √3/2 ) - ( √3/2 )

= [√2/2 + 1/2 - 2√3] /2

= [√2 + 1 - 2√3 ]/2

=[ 1 + √2 - 2√3 ] / 2

Hope helped!

Step-by-step explanation:

Answer 2

Given :  

sin² 30° + sin² 45° + sin² 60° + sin² 90°                            

= (½)² + (1/√2√)² + (√3/2)² + (1)²

= ¼ + ½ + ¾ + 1

= ¼ + ¾ + ½ + 1

= (1 + 3)/4 + (1+ 2)/2

[By taking L.C.M]

= 4/4 + 3/2

= 1 + 3/2

= (2 + 3)/2 = 5/2

[ By taking L.C.M]

sin² 30° + sin² 45° + sin² 60° + sin² 90° = 5/2

[sin 60° = √3/2 ,  sin 45° =1/√2  , sin 90° = 1]                                    

Hence, sin² 30° + sin² 45° + sin² 60° + sin² 90° = 5/2

HOPE THIS ANSWER WILL HELP YOU…