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In a ABC , in which = 90^o , ABC = ^o, BC = 21 units, AB =

Question

In a $△ A BC$ , in which $∠ = 9 0^{o}, ∠ A BC = θ^{o}, BC = 21$ units, $A B = 29$ units, show that $(co s^{2} θ - s i n^{2} θ) = \frac{41}{841}$

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Levi Discussed

In a

△ A BC

, in which

∠ = 9 0^{o}, ∠ A BC = θ^{o}, BC = 21

units,

A B = 29

units, show that

(co s^{2} θ - s i n^{2} θ) = \frac{41}{841}

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Draw a triangle using given instructions:
From figure :

△ A BC

is a right angled triangle

A B^{2} = A C^{2} + B C^{2}

(29)^{2} = A C^{2} + (21)^{2}

841 = A C^{2} + 441

A C^{2} = 400

A C = 20

Find

sin θ

and

cos θ

s in θ = \frac{A C}{A B} = \frac{20}{29}

cos θ = \frac{BC}{A B} = \frac{21}{29}

Now :
LHS =

co s^{2} θ - s i n^{2} θ

= (\frac{21}{29})^{2} - (\frac{20}{29})^{2}

= \frac{41}{841}

= RHS
Hence proved.

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Question Text	In a $△ A BC$ , in which $∠ = 9 0^{o}, ∠ A BC = θ^{o}, BC = 21$ units, $A B = 29$ units, show that $(co s^{2} θ - s i n^{2} θ) = \frac{41}{841}$
Answer Type	Text solution:1
Upvotes	150