Question

1. Evaluate: Sin2 5° + Sin2 10° + Sin2 80°+ Sin2 85°​

Answer 1

Answer:

we know that :---

sin(90-@) = cos@

using this we get :----

sin80° = sin(90-10) = cos10°

sin85° = sin(90-5) = cos5°

Also we know that :-- sin²@+cos²@ = 1

using all this , we get,

Sin²5° + Sin²10° + Sin²80°+ Sin²85°

= Sin²5° + Sin²10° + cos²10° + cos²5°

= (sin²5°+cos²5°). + (sin²10°+cos²10°)

= 1 + 1

= 2 (Ans)

(Mark as brainlist)

Answer 2

Step-by-step explanation:

• Evaluate
• sin² 5° + sin² 10°+sin² 80° + sin²85°

We know that

$sin \: (90 - \theta) = cos \theta$

So by applying this formula in the we determine that

$sin(90 - 80) = cos80 \: and \: sin(90 - 85) = cos5$

And also we know that

$= > \red{sin ^{2} + cos ^{2} = 1 }....(1)$

So , let us find the value which is as follows

$= > \blue{(sin \: 5 + sin10 + cos10 + cos5 }\\ \\ = > \blue{ (sin5 + cos5) +(sin10 + cos10)} \\ \\ = > \: \blue{1 + 1}...(because \: from \: eq(1) \\ \\ = > \red{ \boxed{ \bold{2}}}$

By using the above identities we determined the value of the expression is 2✓