Question

The value of (1 + tan 20°) (1 + tan 25°)​

Answer 1

Answer:

=2

Step-by-step explanation:

It's a consequence of the following trigonometric identity

(1+tana)(1+tanb)=2+tana+tanb−tana+tanbtan(a+b).(1)

On the one hand we rewrite

tan(a+b)=tana+tanb1−tanatanb

as

tanatanb=1−tana+tanbtan(a+b).(2)

On the other hand setting x=tana and y=tanb in the algebraic identity

xy=(1+x)(1+y)−1−x−y

yields:

tanatanb=(1+tana)(1+tanb)−1−tana−tanb.(3)

If we equate (3) to (2), then we get

(1+tana)(1+tanb)−1−tana−tanb=1−tana+tanbtan(a+b),

from which (1) follows. For a=20∘,b=25∘ we obtain

(1+tan20∘)(1+tan25∘)===2+tan20∘+tan25∘−tan20∘+tan25∘tan(45∘)2+tan20∘+tan25∘−tan20∘+tan25∘12.(4)

hope it helps

Answer 2

Answer:

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