A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th innings

Answer:

यह नगर दक्कन के पठार पर मूसी नदी के किनारे स्थित है। हैदराबाद शहर की आबादी 6.9 मिलियन है, हैदराबाद मेट्रोपॉलिटन रीजन में लगभग 9.7 मिलियन के साथ, यह भारत का चौथा सबसे अधिक आबादी वाला शहर है और भारत में छठा सबसे अधिक आबादी वाला शहरी समूह है।

Answer:

There are complementary and supplementary angles. The first add up to 90 and the second add up to 180. So the complement to 50 would be 90-50.

Step-by-step explanation:

The complementary angle of 50° is 40°.

Step-by-step explanation:

the complementary angle is 40°.

Step-by-step explanation:

AnswEr :

• To Prove :

\tan(9) = \dfrac{( \cos(36) - \sin(36) )}{( \cos(36) + \sin(36) )}tan(9)=

(cos(36)+sin(36))

(cos(36)−sin(36))

• Proof :

I'm taking LHS to Prove this Identity -

\Longrightarrow \sf \tan(9)⟹tan(9)

⠀⠀⠀⠀⋆ tan θ = sin θ / cos θ

\Longrightarrow \sf \dfrac{ \sin(9) }{ \cos(9) }⟹

cos(9)

sin(9)

⠀⠀⠀⠀⋆ we can write 9 = (45 - 36)

\Longrightarrow \sf \dfrac{ \sin(45 - 36) }{ \cos(45 - 36) }⟹

cos(45−36)

sin(45−36)

⠀⠀⠀⠀⋆ sin(A - B) = sinAcosB - cosAsinB

⠀⠀⠀⠀⋆ cos(A - B) = cosAcosB + sinAsinB

\Longrightarrow \sf \dfrac{ \sin(45) \cos(36) - \cos(45) \sin(36)}{ \cos(45) \cos(36) + \sin(45) \sin(36) }⟹

cos(45)cos(36)+sin(45)sin(36)

sin(45)cos(36)−cos(45)sin(36)

⠀⠀⠀⠀⋆ sin(45) = 1 /√2 = cos(45)

\Longrightarrow \sf \dfrac{ \dfrac{1}{ \sqrt{2} } \times \cos(36) - \dfrac{1}{ \sqrt{2} } \times \sin(36)}{ \dfrac{1}{ \sqrt{2} } \times \cos(36) + \dfrac{1}{ \sqrt{2} } \times \sin(36) }⟹

2

1

×cos(36)+

2

1

×sin(36)

2

1

×cos(36)−

2

1

×sin(36)

\Longrightarrow \sf \dfrac{ \cancel\dfrac{1}{ \sqrt{2} }( \cos(36) - \sin(36)) }{\cancel\dfrac{1}{ \sqrt{2} }( \cos(36) + \sin(36)) }⟹

2

1

(cos(36)+sin(36))

2

1

(cos(36)−sin(36))

\Longrightarrow \sf \dfrac{( \cos(36) - \sin(36)) }{( \cos(36) + \sin(36)) }⟹

(cos(36)+sin(36))

(cos(36)−sin(36))

⠀

\therefore \boxed{ \tan(9) = \dfrac{( \cos(36) - \sin(36) )}{( \cos(36) + \sin(36) )}}∴

tan(9)=

(cos(36)+sin(36))

(cos(36)−sin(36))

Answer:

To prove :

cos36° + sin36° / cos36° - sin36° = tan81°

Step-by-step explanation:

STEP 1 :

First, we consider the Left Hand Side (LHS),

STEP 2 :

Now, divide each term by cos36°, we get

STEP 3 :

By trigonometric identities, we know that   [tex]\frac{sin \alpha }{cos \alpha } = tan \alpha[/tex] , so we write

     ⇒          [tex]\frac{1 + tan 36^{0} }{1 - tan 36^{0} }[/tex]

since we rewrite the above equation as

     ⇒          [tex]\frac{1 + tan 36^{0} }{1 - 1. tan 36^{0} }[/tex]

STEP 4 :

We know that tan 45° = 1, the above equation is written as

     ⇒          [tex]\frac{tan 45^{0} + tan 36^{0} }{1 - tan 45^{0} .tan 36^{0} }[/tex]            -----> (1)

STEP 5 :

From the formula,  [tex]tan ( \alpha +\beta ) = \frac{tan \alpha + tan \beta }{1 - tan\alpha .tan \beta }[/tex]       -------> (2)

By comparing the equation (1) and (2), we write

                      α = 45° and β = 36°

STEP 6 :

Hence, tan (α + β) = tan (45° + 36°)

                             = tan 81°

                             = RHS

∴ LHS = RHS

Thus, cos36° + sin36° / cos36° - sin36° = tan81°

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Answer:

most.precious thing in the chapter is

Explanation:

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