Prove that: (sin𝒙 − cos𝒙 + 1). (sec𝒙 − tan𝒙) = (sin𝒙 + cos𝒙 − 1)

Question 30 Prove that : (sin𝒙 − cos𝒙 + 1). (sec𝒙 − tan𝒙) = (sin𝒙 + cos𝒙 − 1)Solving LHS (𝑠𝑖𝑛 𝑥−𝑐𝑜𝑠 𝑥+1) × (𝑠𝑒𝑐 𝑥 −𝑡𝑎𝑛 𝑥) = (𝒔𝒊𝒏 𝒙−𝒄𝒐𝒔 𝒙+𝟏) × (𝟏/𝐜𝐨𝐬⁡𝒙 −𝐬𝐢𝐧⁡𝒙/𝐜𝐨𝐬⁡𝒙 ) = (𝑠𝑖𝑛 𝑥−𝑐𝑜𝑠 𝑥+1) × ((1 − sin⁡𝑥)/cos⁡𝑥 ) = (1+𝑠𝑖𝑛 𝑥−𝑐𝑜𝑠 𝑥) × ((1 − sin⁡𝑥)/cos⁡𝑥 ) = ([1+𝑠𝑖𝑛 𝑥]−𝑐𝑜𝑠 𝑥) × ((1 − sin⁡𝑥)/cos⁡𝑥 ) = (𝟏+𝐬𝐢𝐧⁡𝒙 ) × ((𝟏 − 𝒔𝒊𝒏⁡𝒙)/𝒄𝒐𝒔⁡𝒙 )−𝐜𝐨𝐬⁡𝒙 ×((𝟏 − 𝒔𝒊𝒏⁡𝒙)/𝒄𝒐𝒔⁡𝒙 ) = ((1 + sin⁡𝑥 )(1 − sin⁡𝑥))/cos⁡𝑥 −(1−sin⁡𝑥) = (𝟏 − 〖𝐬𝐢𝐧〗^𝟐⁡𝒙)/cos⁡𝑥 −(1−sin⁡𝑥) Putting 1 – sin2 x = cos2 x = 〖𝐜𝐨𝐬〗^𝟐⁡𝒙/cos⁡𝑥 −(1−sin⁡𝑥) = 𝑐𝑜𝑠 𝑥−(1−sin⁡𝑥) = 𝑐𝑜𝑠 𝑥−1+sin⁡𝑥 = (𝒔𝒊𝒏 𝒙+𝒄𝒐𝒔 𝒙−𝟏)

Question 30 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards

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