Question

sin 15° cos 75° + cos 15° sin 75'
Evaluate:
tan 5°.tan 30°. tan 55' tan 85°
​

Answer 1

1) sin15cos75+ cos15sin75

Here cos75 can be written as cos(90-15)

So cos(90-15) can also be written as sin15.

So cos75=sin15(equation 1)

Also sin75 can be written as sin(90-15) which can again be written as cos15.

So sin75=cos15(equation 2)

Substituting equation 1&2 in the question, the question becomes:

sin15×sin15 + cos15×cos15

=sin²15+cos²15

=1. (since sin²x+cos²x=1)



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2)NB: I think the second question should be:

tan5°tan35°tan55°tan85°

2) Here, tan85 can be written as tan(90-5) which can again be written as cot5(equation 1)

Also tan55° can be written as tan(90-35) which again can be written as cot35°(equation 2)

Substituting equation 1&2 in the question

tan5°×tan35°×cot35°×cot5°

Since cotx ×tan x=1

The answer is 1.

Answer 2

1) sin 15° cos 75° + cos 15° sin 75°

= sin(15+75) --- by identity (1)

= sin90

= 1

2) tan 5°.tan 30°. tan 55°. tan 85°

= tan (90-85).tan85°.tan(85-30).tan30

= (cot85°.tan85°)( tan(85-30).tan30)

=tan(85-30).tan30

=tan55.tan30

=tan55/√3

hope it helps .....

plz mark me the brainliest.......

and i think you should recheck the 2nd question