find the value of tan 20 plus tan 45 plus tan 20 tan tan 45
Answers
Answer:
Answer:
1
Step-by-step explanation:
\tan (20^{\circ \:})\tan (40^{\circ \:})\tan (45^{\circ \:})\tan (50^{\circ \:})\tan (70^{\circ \:})tan(20
∘
)tan(40
∘
)tan(45
∘
)tan(50
∘
)tan(70
∘
)
\mathrm{Use\:the\:following\:trivial\:identity}:\quad \tan (45^{\circ \:})=1Usethefollowingtrivialidentity:tan(45
∘
)=1
=\tan (20^{\circ \:})\tan (40^{\circ \:})\cdot \:1\cdot \tan (50^{\circ \:})\tan (70^{\circ \:})=tan(20
∘
)tan(40
∘
)⋅1⋅tan(50
∘
)tan(70
∘
)
\mathrm{Simplify}Simplify
=\tan (20^{\circ \:})\tan (40^{\circ \:})\tan (50^{\circ \:})\tan (70^{\circ \:})=tan(20
∘
)tan(40
∘
)tan(50
∘
)tan(70
∘
)
\tan (20^{\circ \:})\tan (40^{\circ \:})\tan (50^{\circ \:})\tan (70^{\circ \:})tan(20
∘
)tan(40
∘
)tan(50
∘
)tan(70
∘
)
\mathrm{Refine\:to\:a\:decimal\:form}Refinetoadecimalform
=1=1
Alternative Method:
tan20° tan40° tan45° tan50° tan70°
⇒ tan(90° - 20°) tan(90° - 40°) × 1 × tan50° tan70°
⇒ cot 70° cot 50° tan 50° tan 70°
Simplify;
1