Question

(1+сot A - cosec A)(1+tan A + sec A)= 2​

Answer 1

$hence \: proved$

Answer 2

To prove :-

• ( 1 +cotA - cosecA )( 1 + tanA + secA ) = 2

$\huge\bf{Answer :}$

• Taking L•H•S

( 1 + cotA - cosecA )( 1 + tanA + secA )

⇒ { 1 + ( sinA/cosA ) - ( 1/sinA ) } × 1 + ( sinA/cosA ) + ( 1/cosA)

⇒ { ( sinA + cosA - 1 ) / sinA } ( cosA + sinA + 1 ) / cosA

⇒ { ( sinA + cosA )² - 1 } / ( sinA cosA )

⇒ ( 1 + 2 sinA cosA - 1 ) / ( sinA cos A )

On cancelling ( sinA + cosA )² by ( sinA + cosA ), we get :

1 + 2 - 1 = 2 = R•H•S

Hence, proved.

[ Identity used : sin²A + cos²A = 1 ]

$\huge\bf{Extra\: Information :}$

• The word Trigonometry is taken from the 3 Greek words, which were "Tri" meaning three, "gon" meaning Sides, and "metron" meaning measure.
• Trigonometry is the branch of the mathmatics that deals with the study of relationship between the angles and sides of a triangle ( right angled traingle ).
• Trigonometry is used to examine the heights and distance of the objects without actually measuring them.
• Some of the abbreviations used in Trigonometry :-

1. Sin : Sine
2. Cos : Cosine
3. Tan : Tangent
4. Cosec : Cosecant
5. Sec : Secant
6. Cot : Cotangent