Question

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Find the value of

( 1 + tan20°) (1 + tan25°)

Answer 1

(1+tan 20)(1+tan 25)-2

=1 + tan 25 + tan 20 + tan20 × tan25 - 2

=tan 20 + tan 25 + tan20 × tan 25 -1

using tan(A+B)=(tan A + tan B)/(1-tan A×tan B)

⇒tan(A+B)×(1-tan A×tan B)=tan A+ tan B

take A=20, B=25

⇒tan(20+25)×(1-tan 20×tan 25)=tan 20 + tan 25

⇒tan(45)×(1-tan 20×tan 25)=tan 20 + tan 25

⇒1×(1-tan 20×tan 25)=tan 20 + tan 25

⇒1 - tan 20×tan 25=tan 20 + tan 25

⇒tan 20 + tan 25 + tan 20 × tan 25 - 1 = 0

Answer 2

given

( 1 + tan20°) ( 1 + tan25°)

using trigonometry properties

{ ( 1 + tanA)(1 + tanB) =2

if A + B = 45° }

so

value of (1 + tan20°)(1 + tan45°) = 2

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Hope it may Help you.✌️